The experienced goalkeeper has played second fiddle to Thibaut Courtois this season as the Belgian has cemented his place as Mourinho’s first-choice at Stamford Bridge.
At the age of 32, Cech feels he can’t spend any more time on the bench as he approaches the closing stages of his career and is wanted by clubs across Europe.
Premier League rivals Arsenal and Manchester United are also monitoring the situation and the Special One admits he couldn’t block a move to another English club.
"If it's in my hands he would never go, would never go to big clubs with fantastic teams, big candidates to win the Premier League, but it's not in my hands," Mourinho told talkSPORT.
"My perfect scenario is that he stays with us. I think he belongs to this club, this club belongs to his history and to his life, too.
"He is a fantastic keeper, fantastic dressing room and squad man. I tried to prove the respect I have for him. I played him in the cups, gave him matches in the Premier League.
"I can imagine that a 32 or 33-year-old keeper feels young and feels the passion to play every game."
Arsenal manager Arsene Wenger refused to answer questions on his possible interest in Cech when quizzed by reporters last week.
United are putting plans in place for the possible departure of David De Gea as he considers an offer from La Liga giants Real Madrid.