The England defender is out of contract at the end of the season and has struggled to hold down a regular place in Mourinho's starting XI this season.
Former Arsenal striker Thierry Henry has recently revealed that he would be happy if Cole joined him in the MLS with New York Red Bulls in the summer.
And the Portuguese thinks that Cole's head may have been turned.
Mourinho said: "Yes, he (Cole) has (got a future at Chelsea), but maybe Thierry has a better proposal.
"Maybe Thierry is doing with Red Bulls the same as David (Beckham) is doing in Miami. Maybe he's buying Red Bulls! I have to ask Thierry Henry (what's happening with Cole)."
Cole could return for Chelsea on Saturday against Newcastle United in the Barclays Premier League.