Bravo has had a mixed season at the Etihad Stadium but Caballero insists there is no animosity between him and Bravo.
"It's not been an easy week for him but his behaviour is fantastic. He supports me and we are working really hard and he has a competitive mind, so he's doing very well," said Caballero.
"Claudio is a fantastic player, a fantastic keeper and we have to respect him because he is probably the keeper with more titles in his country in the last two years."
They return to action at Bournemouth on February 13 and Caballero has been given no hint of whether he will remain in the side.
"When we train during the week we receive the same indication," he added.
"Whether it's Claudio or me when we train we receive the same information, so we are ready to play and we don't have a difference with the boss and the rest of the players.
"I was always waiting for the cup but now I am ready for every single game. I will try to work really hard for the rest of the week but he always makes the decision for the team."