"Every year there is a challenge. If you are going to be in the team you are going to have to do better than the other guys in the team," the 32-year-old Cech told reporters during Chelsea's pre-season tour in Austria.
"I don't want to be on the bench. This is why I am trying to do everything to be in the team. I don't want to talk about ifs and buts. Let's see how I am going and what happens."
Mourinho this week hailed 22-year-old Belgium international Courtois, who spent three years at Atletico, as "the best young goalkeeper in the world".
He insisted he wanted to keep Cech and that even if he might be unhappy "the Chelsea fans will be happy, and they're more important than any player".
Cech, who missed the latter part of last season with a dislocated shoulder, returned to action in the 1-1 friendly draw with Wolfsberger in Austria on Wednesday.
"Obviously Jose Mourinho will make his choice and decide how his team is going to look for the first game, second game, third game, whatever game," Cech said.
"It is up to us players to show we are ready to play and make him pick us. I am not any different. I am doing everything I can to make him pick me," said the Czech keeper who has been at Chelsea for 10 years.
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