The Super Lig side have offered Yedlin, 27, a three-and-a-half-year deal and are pushing for an answer from the experienced defender.
Yedlin's Newcastle contract is up in June, and he has previously expressed his desire to extend his stay at the Premier League side.
However, sources have told ESPN he is now weighing up the offer from the Super Lig side.
Yedlin's preference has been to sign a new deal at Newcastle, sources have told ESPN.
After one season at Spurs -- which included a loan spell to Sunderland -- he moved to Newcastle for £5.3 million.
To date he has made six Premier League appearances for Newcastle during the 2020-21 season.