Courtois was chosen ahead of Cech for the opening match of Chelsea's Premier League season on Monday, hinting that manager Jose Mourinho plans to use the Belgian as his first choice.
Cech, who has been the number one keeper at the club for a decade, is widely regarded as being too good to sit on the bench, but Courtois believes that the 32-year-old's presence will benefit him.
"I want him to stay. Even if he doesn't play he can be a lot of help to me in training," Courtois is quoted as saying by PA.
"I can still learn from him because he has a lot of experience, he can give me good tips about the Premier League, things I might not know at the start. He is nice to me. We are training very well and he is still proving he is a great goalkeeper.
"For the team it is better for us to have two good goalkeepers. I don't have a problem if he stays. Hopefully I can play well and stay in the team."
Courtois, 22, impressed on his Premier League debut as Chelsea cruised to a 3-1 win over Burnley at Turf Moor.