The Argentine shot-stopper, signed from Malaga in July, started for City on Sunday as they suffered a 3-0 loss to Arsenal in the Community Shield.
Caballero said he is desperate to retain his spot ahead of Sunday's league clash at Newcastle United.
"Yes I want to be number one," he said.
"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 defend their title while starting to challenge for the UEFA Champions League.
"We have a strong team," he said.
"We are the Premier League champions, with very good players, but we have things we need to prove.
"[Manager] 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."
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