Caballero joined City from Malaga earlier this summer with Manuel Pellegrini a big fan of the goalkeeper having worked with him during his time in charge of the Spanish side.
The Argentine has impressed so far in pre-season and he is determined to fight for the No.1 shirt with Hart in the new Premier League season.
"I know the situation now but I will fight to play," said Caballero. "The decision will be down to the coach, the boss.
"I have trained well and I will fight.
"I know my position, but I want to try hard to fight for this position.
"Joe is a fantastic goalkeeper, but I've come to play. I want to try and take my opportunity.
"It will be difficult, yes, but City are a big club and it's a big opportunity. I want to try in every way I can to play."
Caballero admits the presence of Pellegrini played a huge role in his decision to leave Malaga for City this summer.
"It was a crucial part of me coming to City knowing him from before and having played for him," added Caballero. "He was a very important figure in me coming to Manchester City," he said.
"I had no doubt about the move. I think it was necessary for my career, for my life and for my family. It's fantastic for me.
"He hasn't given me any promises, no, I only know that he wanted me. I came here for the best opportunity for my career.
"I don't know if I play in the cup or other tournaments, I don't know anything. But of course I am confident.
"Goalkeepers are a different type of player and I believe in myself."