After ousting Joe Hart as City’s main goalkeeper, the Chilean struggled for form and was soon replaced by Willy Caballero.
But Bravo is determined to battle for his place at City and said he has been used to competition throughout his career.
"My future is still linked to City for a long time," he told AS ahead of Ederson’s move to the club.
"You always have competition at this level. It happened to me at Colo Colo, in the national team, at Real Sociedad, at Barcelona, at City -- all my life has been a competition.
"I knew this was going to be the scenario for a while, but this is not something that worries me. Football is like this at the highest level and more so in these powerful clubs.
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"Wherever you look, you have a selection of the best in the world."
Bravo also admitted that his first season at City had not gone to plan but he remained defiant nonetheless.
"Sometimes it's like this -- one season things don't go as planned," he added.
"I had two successful seasons at the highest level, and I've just experienced one where we did not achieve what we aimed for from a team standpoint, but one thing does not rule out the other.
"I've always been consistent and persevered on the aims that I set myself. It hasn't been the year that I expected, but I hope the next one will be much better."
The Chilean dismissed suggestions that he had struggled to cope with the physicality of the Premier League after a decade playing in Spain.
"Many people think so, that it was down to adapting but I don't think so," he said. "There has been a tendency to link my name with that of the functioning of all the team. I don't want to delve into this.
"The whole team did not function as it should have during certain times of the season, but that is in the past."
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