Courtois, 22, who has returned to Chelsea from a successful loan spell with Atletico Madrid, was Mourinho's choice for the club's Premier League opener on Monday, a 3-1 win at Burnley. (Agencies)
Cech has been Chelsea's first choice keeper since joining the club 10 years ago, part of three Premier League winning squads and the 2012 Champions League winning team.
Asked whether Courtois was now the first choice for the rest of the season, Mourinho said he didn't want to look too far ahead.
"I don't like the word 'for the rest of the season'. He is not my first choice for the rest of the season. He was my first choice today and I think he played a game that was good enough to be my first choice in the next game," Mourinho told reporters.
The Chelsea boss said that Courtois would have to remain on top of his game to keep his spot in the side given the competition he faces.
"When you have on your side working like a top professional somebody like Petr, if you don't perform you are in trouble. I am not in trouble I am safe, Chelsea is not in trouble, Chelsea is safe, they are both fantastic goalkeepers," he added.
Mourinho said he expected that Cech would react in the right way to the disappointment of being left out.
"I want to keep (Petr) the club wants to keep him and hopefully he stays," he said.
"I know Petr for 10 years, I know that he won't relax, he won't sit in a chair and say 'I have no chance', I think he will be exactly the opposite.
"I am expecting him on Wednesday to go to the training ground and to be a top professional and to fight to be back in goal," he added.
Courtois, 22, who has returned to Chelsea from a successful loan spell with Atletico Madrid, was Mourinho's choice for the club's Premier League opener on Monday, a 3-1 win at Burnley.