The 19-year-old has attracted interest from a host of Premier League clubs, but is ready to snub a transfer in order to continue his development.
Despite his young age, the midfielder has already made his international debut for the Netherlands national team and is highly rated by Blues interim boss Guus Hiddink.
Incoming City manager Pep Guardiola is set to make a move for the player when he replaces Manuel Pellegrini at the end of the current campaign.
Bazoer has hinted that he is aware of interest from a number of European elites, but is ready to snub a big money move in favour of continuing his development.
“I prefer to stay at Ajax until 2020. My development is more important than money,” he said.
He has already featured 34 times in all competitions for his side this term, so far managing to score five goals while providing another four assists.