The 32-year-old joined the Ligue 1 champions from Napoli for just short of £60 million in the summer of 2013, and has gone on to usurp Sweden great Zlatan Ibrahimovic as the club's all-time leading goal scorer.
However, it is rumoured that Neymar's arrival in France in 2017, along with Kylian Mbappe's growing influence at the club, has seen the former Palermo man became increasingly disillusioned with life at the Parc des Princes, as well as being tempted by a move to Maurizio Sarri's Juve.
There is also believed to be interest from sides in the Premier League, with Manchester United keen to add some much-needed firepower to their forward line.
LIVE BLOG
22.50 BST: Folks it's that time of day we call time on another edition of our live Transfer Talk blog and hit reset with a brand new paper round in a few hours before coming back to do the whole thing again tomorrow. Thanks as always for checking in, we'll see you next time!
22.30 BST: Arsenal boss Unai Emery is feeling pretty good about his team's position in the Premier League if you believe reports in The Mirror. How good? Well the Spaniard has his team sitting third in the table and is so happy with his squad that the report suggests the Gunners won't lift a finger in the winter window.
21.40 BST: A report on Football Insider suggests that Liverpool are willing to listen to offers for 20-year-old midfielder Herbie Kane. The report says that the Premier League leaders were hopeful that Kane could rise into their senior team ranks, but now realize "there is too much competition blocking his senior path."
20.55 BST: Napoli are ready to offer Dries Mertens and Jose Callejon new deals to keep them at the club for the long-term, reports Gianlucadimarzio.com. The attacking duo are both out of contract in June of 2020 and the report says Napoli are ready to make a lucrative offer to both to extend their stays in Serie A.
19.40 BST: On-loan Arsenal defender Mohamed Elneny could soon be trading Turkey for Italy, according to Gazzetta dello Sport. Struggling Milan are mired in the bottom half of the Serie A table and the report says the Rossoneri will make a January approach for the 27-year-old as they try to right the ship.
18.45 BST: Bad news for Inter Milan and Fiorentina, as Calciomercato reports that Udinese No. 10 Rodrigo De Paul -- a summer target for both -- has signed a new deal to keep him with the club until 2024. The reports says Milan were also plotting a January swoop, but that prospect will become much more difficult and expensive in light of the new deal for the Argentine.
17.28 BST: Real Madrid want Kylian Mbappe, that's no secret, but Le10 Sport claims that the Spanish club are ready to offer the PSG striker around €35m a year to sign.
That equates to roughly €650,000-a-week and not even Gareth Bale earns that much at Madrid! In fact, Barcelona star Lionel Messi's estimated €40m per year would be the only wage packet in the world to exceed it...
16.14 BST: Right then... Tottenham are struggling; Jose Mourinho doesn't have a job. See the link?
Yes, Soccerlink over in France reports that Spurs are tentatively looking for a new manager now just in case they have to sack Mauricio Pochettino soon. And that the club have already been in contact with Mourinho to check he'd be up for it.
Mourinho loves the Premier League and with Chelsea and Man United already on his CV, a move to north London might make sense in the end. But usually things start going south for the Portuguese in the third season.
15.13 BST: Olivier Giroud is doing well for France, but isn't playing for Chelsea. That has to change.
14.09 BST: Manchester United are giving their young players a chance this season but Angel Gomes, Tahith Chong and James Garner may depart on loan in January.
"Three lads could have possibly gone on loan -- Angel Gomes, Tahith Chong and James Garner -- but he [Ole Gunnar Solskjaer] wanted to keep them here and have a look at them on tour," academy performance manager Les Parry told the club website. "So a decision will be made, no doubt, for January as well. Hopefully, all three will be in the first team and not going anywhere.
"As we know at this club, lads have got into the first team and a lot of it has been through circumstances they've got no control over. They've been presented with an opportunity and they've taken the opportunity so now a couple of them are regulars on the teamsheet each week. We've had opportunities that have cropped up from nowhere. That's football."
13.06 BST: Real Madrid's €60m striker Luka Jovic is "is having a nightmare for club and country" says Sport.
The Serbian has not scored yet and there is talk that the 21-year-old is so unhappy in Madrid that he's ready to move on loan in the winter window.
12.22 BST: Fenerbahce striker Vedat Muriqi has been attracting the interest of Tottenham but Turkish newspaper Star reports that Bournemouth are getting involved too.
Muriqi, 27, could replace striker Callum Wilson if he departs in a £50m move to Man United. Prepare to hear more about the Kosovo international in January.
11.43 BST: Manchester United are in trouble. But how can they be fixed?
10.15 BST: Real Madrid made a move to sign Lucas Hernandez long before Bayern Munich landed the centre-back for €80m this summer, but it was a non-starter according to the Frenchman.
"Real had already made a move for me, it's true, but not this summer," he told France Football. "And I wouldn't go there. Not after having worn the colours of Atletico for such a long time."
09.24 BST: Never let it be said that managers don't go with what they know. Juventus boss Maurizio Sarri wants Emerson Palmieri and N'Golo Kante from his former club Chelsea, according to the The Express.
08.46 BST: There have been a lot of FC Salzburg players featured in this column over the past few weeks and now another has been linked with a move to Barcelona by Mundo Deportivo.
If you haven't heard of Karim Adeyemi, 17, it's because he's been playing for the club's feeder side FC Liefering in the second tier of Austrian football. However, the striker has played in the UEFA Youth League for Salzburg where he has impressed. And that's caught the eye of the Catalan giants.
08.00 BST: Manchester United are prepared to back manager Ole Gunnar Solskjaer in the January transfer window but are warning that they will not overpay for players just to save the season, sources have told ESPN FC.
The Glazers and executive vice-chairman Ed Woodward accept that Solskjaer's squad has been left short in midfield and up front after the summer departures of Romelu Lukaku, Alexis Sanchez and Ander Herrera.
Juventus striker Mario Mandzukic, 33, remains an option to provide competition for Marcus Rashford, Anthony Martial and Mason Greenwood up front but has been told he will need to drop his wage demands to secure a move. Midfielder Ivan Rakitic is available from Barcelona, but sources have told ESPN FC that a move to United is unlikely because of family reasons.
Deals for long-term targets such as Leicester playmaker James Maddison, West Ham midfielder Declan Rice, Aston Villa midfielder John McGinn, Bournemouth striker Callum Wilson and Lyon's Moussa Dembele will also be explored, but there is an acceptance that most of the next round of recruiting will have to wait until next summer.
PAPER TALK (by James Capps)
Chelsea lead chase for Charlie
Chelsea are hoping to beat Southampton to the signing of highly-rated teenager Charlie Allen from Northern Irish champions Linfield, according to reports in the Express.
The 15-year-old has already had trials at Manchester City and Tottenham after breaking into the Linfield team, and Blues manager Frank Lampard is reportedly keen to be the next Premier League manager to cast his eye over the youngster. Premier League rivals Southampton and Norwich -- as well as Scottish giants Rangers -- are also keeping tabs on the player.
But Lampard is hoping his record of developing and fast-tracking young players into senior football could be a game-changer in negotiations for the Northern Ireland Under-17 international, who was included in his club's Champions League squad for their two-legged tie against Rosenborg in the summer.
Bayern and Monaco weigh up Waldschmidt
Bayern Munich and Monaco are interested in signing striker Luca Waldschmidt from Bundesliga side Freiburg, according to Calciomercato.
The 23-year-old made his Germany debut in a friendly against Argentina last week, as well as his competitive bow in Die Mannschaft's 3-0 victory in Estonia on Sunday night.
The former Hamburg man forced his way into the Germany setup following a strong start to a season that has seen him notch four goals in his opening seven league games, and that form has reportedly alerted Bundesliga heavyweights Bayern, who are on the lookout for a long-term successor to Poland forward Robert Lewandowski.
Monaco, meanwhile, have had a poor start to their Ligue 1 campaign, and are in need of a scoring touch to boost them up the table, and could be tempted by a January swoop for the Eintracht Frankfurt academy graduate.
- When does the transfer window reopen?
- All major completed transfer deals
Tap ins
- The Sun says Tottenham Hotspur chairman Daniel Levy shocked fans at a Supporters' Trust meeting by admitting that boss Mauricio Pochettino has been left with players he doesn't want at the club, after failing to find buyers for a number of wantaway stars. The likes of Christian Eriksen, Toby Alderweireld and Danny Rose could all leave north London for nothing when their contracts expire in the summer of 2020.
- Calciomercato claims Manchester City manager Pep Guardiola is eyeing up a swoop for Real Sociedad midfielder Mikel Oyarzabal, as the Premier League champions search for a long-term replacement for the outgoing David Silva. The 22-year-old has been involved in six goals in just eight games so far this season.
- An agreement is yet to be struck that will see Napoli winger Jose Callejon remain at the Serie A runners-up, and Calciomercato claims Rafa Benitez wants to bring his fellow Spaniard to Chinese Super League side Dalian Yifang. The 32-year-old joined Carlo Ancelotti's side in 2013 and has made more than 300 appearances for the club.
