Cech has been heavily linked with a move away from Stamford Bridge in recent weeks after falling behind Thibaut Courtois in the pecking order this term.
Arsene Wenger and Brendan Rodgers, who are both keen to replace Wojciech Szczesny and Simon Mignolet as first-choice stoppers respectively, are expected to make a £7m bids for Cech in January.
However, Mourinho claims he will do everything he can to convince the Czech international to stay.
"The most important thing is what he brings to the team on the pitch, which is top quality," Mourinho said.
Petr Cech Player Profile
I have to feed his ambition to keep him
Jose Mourinho
"When Courtois was injured against Arsenal and Petr Cech comes to play on minute 20, I was so calm. I wasn't worried about a change of goalkeeper. So when you have on the bench a super goalkeeper like Petr Cech this is the most important thing.
"Obviously he wants to play, which is why sometimes I make him play. I have to feed the natural ambition of somebody who feels he is a top goalkeeper.
"I have to feed that ambition to keep him... I'm not saying happy happy, because to be happy a player must play every game... but at least to make him feel that we like him, we respect him and we need him."
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