The 20-year-old is currently in the middle of a loan spell at League One club Portsmouth, where he has featured in 43 of their 45 league games.
His performances between the sticks for the Fratton Park outfit have not gone unnoticed, with clubs in the Championship showing interest in securing his services.
Paul Heckingbottom’s Sheffield United are one club showing interest in Bazunu, and they will try to sign the player in the summer irrespective of whether they go up at the end of the season or are forced to try again.
Bazunu wants to play in the Premier League, but the lure of playing regularly might make him decide in favour of a move to Bramall Lane.
Preston North End are also interested in the shot-stopper and it is claimed that his admirers believe a deal can be done.
They know Bazunu does not want to sit on the bench at Manchester City and feel he can be snapped up.
The 20-year-old has managed 16 league clean sheets for Portsmouth thus far this season.
His contract with Manchester City runs until the summer of 2024.