Courtois compared the situation to that of Mourinho, who won the league in 2014-15 but was sacked the following season after a poor run of results.
"We are ready to fight for the coach," Courtois told Standard Sport. "I remember what happened two years ago under Jose Mourinho and things started to be said, there were stories about the dressing room without knowing what was happening.
"We are happy to show that we are ready to fight. We all know what would have happened (more debate over Conte's future)if we had lost against Watford."
Courtois, 25, dismissed reports regarding player unrest over the manager's training methods.
"Every manager has his own routine. With Antonio we do a lot of tactical sessions and drills. We are fine with it," the Belgian said.
"Last season we were champions with his way and we trained much more than this season, so I don't know why somebody would complain. It's not as if we don't like to train."
Fourth-placed Chelsea face Everton in the League Cup fourth round on Wednesday before travelling to 19th-placed Bournemouth in the league on Saturday.
(Reporting by Aditi Prakash in Bengaluru; editing by Sudipto Ganguly)
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