The Belgium international spent the last three campaigns on loan at La Liga champions Atletico Madrid, but has returned to Stamford Bridge to challenge long-time number one Petr Cech for a starting berth.
It was Courtois who got the nod ahead of Cech for Chelsea's Premier League opener at Burnley on Monday - a 3-1 victory - and the 22-year-old is reluctant to give up his place.
"I know that Petr is a great goalkeeper, so there is a lot competition," he is quoted as saying in The Mirror. "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's nice that he put faith in me and it's 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."
Courtois also revealed he was only told he would be starting an hour before kick-off at Turf Moor.
"He [Mourinho] said it an hour before the game," he added. "It was nice. I came here obviously to play."
