The 18-year-old attacker has made an impression since breaking into the first-team squad at Juventus this season.
He is yet to score for the Bianconeri but recently made his debut for Turkey and scored his first international goal for his country.
His performances have attracted the attention of Liverpool sporting director Jorge Schmadtke, who has recommended the forward to manager Jurgen Klopp as a potential signing.
Juventus are pushing to hold on to him and even signed him up on a new deal in the summer, but according to Italian daily Tuttosport (via Tutto Mercato), that stance could change.
For the moment, Juventus do not want to sell the forward and want to invest in him as their future.
However, they could rethink their position if an offer in the region of €35m to €40m arrives on their table.
The Serie A giants are looking at a midfield overhaul in the next couple of windows and need cash to bring in players.
In the face of a big offer, they could be forced to sell Yildiz soon to raise funds and balance their financial fair play calculations.
Arsenal are also amongst the clubs who are believed to be interested in snapping up the forward.