The 22-year-old got the nod to start in the Premier League opener against Burnley on Monday after returning from his three seasons on loan at Atletico Madrid.
Chelsea boss Jose Mourinho has said he wants the 32-year-old Cech to fight for the position he has made his own since joining the club in 2004.
Cech has yet to publicly comment since losing his starting place, but Courtois said he hoped to tap into the Czech Republic international's immense Premier League experience.
"I want him to stay. Even if he doesn't play he can be a lot of help to me in training," said Courtois, who gave an assured display despite conceding the opening goal in the 3-1 win over Burnley.
"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."
Mourinho has given Courtois, who won the La Liga title and played in the Champions League final last season, no guarantees that he will remain first choice.
"Always when you are here you have pressure to perform because you are playing in a top team," added Courtois.
"There is always a pressure to win games and to be important and I am trying to do that in every game that I play.
"I came here obviously to play. I know that Petr is a great goalkeeper so there is a lot of competition, but when you come back from a successful loan you hope to play.
"Otherwise, it would maybe have been better for me to go to another team.
"It is nice that he put faith in me and it is for me now to prove his faith is right.
"I need to work hard in every training session and game to gain the confidence of my team-mates and the manager."
In all honesty I think he does want Cech to stay so long as he is No.1. Personally I find it awkard and can see Cech going. Courtois is certainly confident but he has youth on his side and could be Chelsea No.1 for the next 10 years. Jose wants a settled side and having a GK who is happy and performs well would be a position he hasn't got to worry about whereas no he has friction between two top GK's. I like Cech, he still is a top keeper but I think Courtois offers more even if he is full of himself. Chelsea still have two other good reserve Keepers. Chelsea need another fullbac so perhaps this transfer can help Jose get one.- crow