Cech has been a mainstay of Chelsea's squad since arriving at Stamford Bridge from Rennes a decade ago.
However, he faces stiff competition for a starting berth this season after Belgium international Thibaut Courtois returned to Chelsea following three hugely impressive seasons on loan at Atletico Madrid.
Courtois is believed to be in pole position to start the campaign as Mourinho's first choice, while Cech's agent claimed last month that there had been interest in his client from Monaco and Paris Saint-Germain.
Mourinho admits he has a tough decision to make but appears to have opened the door for Cech's departure by hailing Courtois and confirming he would be comfortable continuing to use veteran Australian Mark Schwarzer as his back-up keeper, as he did last season.
"Petr is ready to fight for his position but Thibaut is the best young goalkeeper in the world, no doubts about that," Mourinho is quoted as saying by the English media.
"They will fight and for me it's a good problem to have to make a decision.
"We are a club that wants to be strong and wants to have a real possibility of competing for trophies and we want competition for places.
"But I know that Mark Schwarzer is a very good keeper, very stable and a good man, completely ready to be our second goalkeeper like he was last season and to give positive performances if we need him to play.
"So if he's our second goalkeeper, we will feel very safe with him."