The Turkey international and AC Milan are in the middle of a contract stand-off with his current deal expiring at the end of the season.
Calhanoglu’s wage demands would see him become the highest paid player at the club if AC Milan agree, but the Italian giants are unwilling to go above €3.5m per year at present.
Talks are still happening, but Calhanoglu is looking for well over €5m per year and a January exit, with Manchester United having been linked with him, has been mooted.
AC Milan do not want to see him leave on a free transfer next summer, but according to Italian outlet Calciomercato.com, neither party want a January move.
The midfielder is still keen to stay at AC Milan and is looking to break the deadlock in negotiations over a new deal.
The player and the club are not keen to end negotiations by considering parting ways in the January transfer window at present.
It would leave AC Milan with the possibility of seeing the midfielder leave the club on a free transfer next summer.
In addition to Manchester United, Calhanoglu has also been linked with Atletico Madrid and Juventus.