Cech's future at Stamford Bridge has been the subject of speculation this summer with Thibaut Courtois having been recalled from his successful loan stint at Atletico Madrid.
Mourinho has admitted Cech and Courtois will battle out for the goalkeeper's shirt next season as he wants competition for places at Stamford Bridge.
The likes of Monaco and Paris Saint Germain have been linked with moves for Cech, but the 32-year-old claims he is not even thinking of leaving Chelsea.
"I'm staying at Chelsea, that for sure," Cech told Ekipa24 after Chelsea's 2-1 win over Olimpija Ljubljana on Sunday.
"I really don't mind that there are two great keepers at Chelsea. That motivates me ever more.
"You always have to fight if you want to be on great level. And there is not only Courtouis and me, even Matej Delac is showing that he is great keeper."