The 27-year-old has a contract will Il Diavolo but he has not been impressed with the contract offer the club has proposed to him so far.
According to Tuttosport, AC Milan directors Paolo Maldini and Frederic Massara have proposed a wage that is €1 million less than what Calhanoglu would like and they have no intention of increasing their offer.
In the event that the Rossoneri do not qualify for the Champions League, the directors might scrap the deal altogether.
Calhanoglu joined AC Milan from Bayer Leverkusen in 2017 and he has scored 31 goals as well as provided 47 assists in 167 competitive games for the Italian giants.
The Rossoneri are equal third in Serie A with Napoli and Juventus on 66 points after 33 rounds.