Mourinho's comments come after Cech's agent, Viktor Kolar, confirmed that the 32-year-old has been in talks with numerous "interested parties".
Cech has only been included in Chelsea's starting line-up five times this season as Thibaut Courtois has cemented his place in the team following a plethora of outstanding performances in goal.
While Cech has been heavily linked with a move to Arsenal, Mourinho is hoping that the Czech Republic international will stay with the Blues and not join their London rivals.
"I have to say, yes, I am optimistic that he can be here next year," Mourinho told reporters. "I keep saying the same. I want my best players, Petr is one of my best players. I would like him to stay.
"I don't know if it's absolutely true what the agent is saying. Maybe it is but he has a contract with Chelsea and we have an important say in his decision."