Hart has firmly re-established himself as City boss Manuel Pellegrini's first-choice keeper after a spell on the sidelines last season.
The England stopper has played in 18 of the Premier League champions' 19 top-flight fixtures this term, and also started all six of their UEFA Champions League group games.
However, the 27-year-old knows he cannot let his standards slip with Caballero - a close-season signing from Malaga - waiting in the wings.
"There is always a threat at this place - we wouldn't be the club we are if we didn't feel that people who weren't performing in their position weren't replaceable," Hart told The Mirror.
"I am replaceable, as everyone is, and you have to perform to high levels.
"Willy is a fantastic keeper and when he has stepped in he has done well. He is a great person too.
"His work ethic and how he has been with me has been fantastic.
"We have a good relationship but if anyone is going to push me, it's got to be me."
Following a run of eight wins and two draws from their last 10 Premier League games, City sit just three points adrift of table-topping Chelsea before their New Year's Day clash with Sunderland.
And Hart remains upbeat about their chances of overhauling the Londoners and retaining their title.
"We are starting to flow now - starting to get results, score goals and defend how we wanted to defend. We are getting there," he added.
"And we are strong and confident. We have stuck by each other, and the manager has stuck by us and we are getting the rewards for that.
"We are a team of winners and we will stick it through. We have got a good manager, so hopefully we can steer our way through successfully like we have done in the past."
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