Cole's contract expires in the summer but the player's representatives continue to have dialogue with the club.
However, his participation in the World Cup finals in South Africa is looking particularly vulnerable.
Cole has fought his way back to fitness after a serious knee injury but is yet to hold down a regular place in Carlo Ancelotti's side.
He started on the bench for the FA Cup fourth-round tie against Preston at the weekend but he will play against City, and Ancelotti insists he can still convince Fabio Capello to take him.
"It's not too late for him," said Ancelotti. "There are a lot of games until the end of the season and he has the time to show his quality.
"I think that he's doing well. The last game against Sunderland he did very well without the ball, moved very well. He has to improve when he has the ball.
"He has the quality to do better when he has the ball. But he has the time. Fabio has not asked me about him. I haven't spoken to Capello."