Courtois, who is back in London after a successful loan at Atletico Madrid, was selected ahead of long-standing number one Cech for the season-opening win at Burnley.
The 22-year-old Belgian caught the eye with some smart saves in the 3-1 victory and seems likely to continue for the Blues' next Barclays Premier League outing against Leicester on Saturday.
The situation has led to speculation Cech, 32, who joined the club a decade ago, could move on before the transfer deadline at the end of this month.
Courtois said: "I want him to stay
Even if he doesn't play he can be a lot of help to me in training.
"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."
Chelsea manager Jose Mourinho has played down suggestions Cech could leave, believing the Czech will want to fight for his place.
He has also offered no guarantees to Courtois that he will remain first choice.
Courtois, who spent three years with Atletico and won a league title last season, accepts that situation but is determined to make the most of the opportunity Mourinho has given him.
He said: "Always when you are here you have pressure to perform because you are playing in a top team.
"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."
Source : PA
Source: PA