The Italian giants travel to Parkhead on Thursday for the first group stage match, but may have to do so without their creative Turkish ace.
According to reports in Italy, the player won't recover from an injury which left the player in crutches.
Calhanoglu picked up a knock in training today and it could mean Stefano Pioli is without a player who has been key to the club’s strong start.
The 26-year-old, who has 50 caps for Turkey, has started six of seven matches this season with Milan making an unbeaten start to the season.
He has left his best form for the European stage, hitting four goals in the three qualifying games.
Calhanoglu, a €24million signing from Bayer Leverkusen in 2017, also started the recent 2-1 win over rivals Inter Milan.