Zaniolo has been linked with moves to Tottenham Hotspurs and AC Milan but Roma is yet to receive a concrete offer from either club.
The 23-year-old still has 18 months remaining on his contract at the Stadio Olympico.
Zaniolo was left out of the Roma squad for Sunday's 2-0 win at Spezia, with sporting director Tiago Pinto saying before the game that the Italy international had decided not to feature.
Zaniolo has scored one goal in 13 Serie A appearances this season.
Mourinho said: "The director spoke before the match, and he did it well. The important thing today is to have won with a good team performance.
"I have my opinion and I think he will stay here in February, but the market is open and he wants to leave.
"Showing desire doesn't mean leaving. Usually when a player wants to leave it means that there are important offers behind it, but that's not the case.
"There's nothing on the table, nothing the club can accept."
Speaking to broadcaster DAZN, Mourinho added: "I have a very good relationship with him, I have always tried to help him. He has made a maximum effort and for this reason I have always defended him, even when he has been criticised for the few goals and assists."
"Right now he wants to leave."
"It's something I have to accept, but where's the offer?
"If he leaves, someone has to come in return. The situation is unacceptable, and I'm sorry that in this story Tiago Pinto comes out as the villain of the story. He's not the villain of the story but tries to defend the interests of the team."