The champions were on course for a third league defeat in a row when they trailed Watford 2-1 at Stamford Bridge on Saturday, but a second-half comeback saw them record a 4-2 victory to instead move back into the top four.
Reports have claimed that Conte's training methods have been called into question by members of the squad this season, leading to speculation that the Italian could leave his role just months after steering the club to the Premier League title in record-breaking fashion.
Chelsea were in a similar situation when they won the title under Mourinho in 2015, with the Portuguese boss being sacked by December of the following campaign, but Courtois insists that they are striving to save Conte.
"We are ready to fight for the coach. 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," he told the Evening Standard.
"There was a moment when we were 2-1 down, we were having difficulties and Watford could have made it 4-1. It was very important to come back to win. In 2015 [under Mourinho] we wanted to fight as well but the game didn't turn out well for us, there was too much bad luck. Sometimes different things happened. But we are showing we want to fight again now, firstly as a group of players. We want to win games.
"We don't want to lose and say we don't care any more. We want to fight for ourselves, too. It is important for us. Some of us remember what happened two years ago and we don't want the same thing to happen. Every manager has his own routine. With Antonio we do a lot of tactical sessions and drills. We are fine with it. 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."
Chelsea, who face managerless Everton in the EFL Cup on Wednesday night, are currently nine points adrift of pacesetters Manchester City.