Bazunu spent last season on-loan at Rochdale.
"That's 100 per cent my aim," he told Sky Sports when asked if he thought he could become City's number one.
"I wouldn't have gone to Manchester City unless I thought I could be the number one goalkeeper.
"Every day, that's what I work towards. That's the goal."
"I speak to Xabi, who is the goalkeeper coach there. I spoke to him today actually, and I like to keep in contact with him", he said.
"During the season, I speak to him once or twice a week and we go over the clips from previous matches and he gives me an insight on what he thinks I can improve on.
"Initially the plan was that I would go in and train with them once or twice a week but because of Covid and all the restrictions that wasn't possible."