The 32-year-old put in a disappointing showing in the Community Shield at Wembley but hopes some hard work on the training ground will see him rewarded
The Argentine shot-stopper, signed from Malaga in July, made his competitive debut for the Premier League champions as they suffered a 3-0 loss to Arsenal in the Community Shield on Sunday.
And Caballero said he is desperate to retain his spot when Manuel Pellegrini's men kick off the defence of their title at Newcastle United on August 17.
"Yes I want to be No.1," he admitted to reporters.
"I will train for the weekend for the next decision to see who starts next. Both of us will train for that chance.
"I came to fight for the number one spot. Sunday at Wembley was an important match for me – I have a chance to play.
"I am happy for this – not for the score. I have been training well but there is no doubt that this was not one of my best games.
"A defeat like this hurts but the most important thing is not to repeat these errors."
Caballero has no doubt City can retain their Premier League crown, but it is in European competition where the Blues have struggled to challenge the established sides on the continent.
However, the shot-stopper is adamant that the Etihad Stadium outfit will be stronger on all fronts when the new campaign gets underway.
"We have a strong team," he declared. "We are the Premier League champions, with very good players, but we have things we need to prove.
"Manuel [Pellegrini] has told all of us that we need to learn game by game, and that we have to start well in the league.
"I think we can win the title again. We have to do what we did last year, to win the league.
"We were the best team in the Premier League. We have to improve in the Champions League and we have a good squad to do that."