Messi's deal at Camp Nou runs until 2021, but sources have told ESPN FC that Barca president Josep Maria Bartomeu has already initiated talks over a new lifetime deal.
Andres Iniesta signed a similar deal with the club in 2017, only to leave for Japanese side Vissel Kobe less than a year later.
Barca do not expect Messi's departure to be imminent, though, despite the forward using his acceptance speech at the Theatre du Chatelet in Paris to suggest he doesn't know how much longer he has left at the top level of the game.
"I'm aware of how old I am," Messi said after winning the Ballon d'Or for a record-breaking sixth time. "And I enjoy these moments so much because I know that retirement is approaching. Time flies."
Messi later added some nuance to his comments by saying that he still feels in great shape.
"I hope, God willing, that I keep playing for many more years," he told reporters after the Ballon d'Or ceremony when asked about retiring. "I'm now 32, though, and will be 33 at the end of the season, so, as I said, everything depends on how I feel physically.
"Right now I feel better than ever on a physical and a personal level, and I hope I can go on for a lot longer."
There is a clause in Messi's contract that would allow him to leave for free at the end of the season, should he wish. He allayed fears that he is about to walk away from Barcelona, though, by saying the small print in his contract is not important.
"Barca know me and know there's no type of problem with these issues," he said. "[My commitment] goes beyond a contract. What I feel for this club is [worth] more than any signature on a piece of paper, so there's no issue."
Eric Abidal confirmed last month that moves were being made to hand Messi a contract extension. Bartomeu has since broached the subject with the player's representatives and the club are hopeful of developments in the not too distant future.
Messi's next contract will be his 10th professional deal with Barca and potentially his last. His latest renewal was signed at the end of 2017.
On the pitch, he remains as important as ever. He scored the winning goal in Sunday's victory at Atletico Madrid and followed up being named FIFA's The Best in September with the Ballon d'Or on Monday.
He first won the Ballon d'Or in 2009 and has now won it on six occasions, edging clear of Cristiano Ronaldo as the award's most decorated player. Juventus forward Ronaldo, who finished third this year behind Liverpool's Virgil van Dijk, has won it five times.