The Republic of Ireland goalkeeper spent last term on loan in League One at Portsmouth, where he impressed between the sticks.
Bazunu is keen to make sure that he is playing football on a regular basis next season and has been looking to again move on from Manchester City.
The goalkeeper is now closing on a permanent move to Southampton, despite Manchester City offering him a big pay rise to pen new deals at the Etihad.
However, Manchester City remain determined to continue to control Bazunu’s future, even after they sell him.
As such they will insist on a buy-back option in the agreement to let the custodian move to the south coast.
Bazunu, 20, was plucked from Irish side Shamrock Rovers by Manchester City in 2019.
He spent the 2020/21 campaign on loan in League One with Rochdale, but will now sink his teeth into Premier League football at Southampton.
The Saints are expected to pay around £10m for Bazunu.
