The youngster kept 16 clean sheets in 44 league appearances at Fratton Park, and faces an important decision for his career this summer.
Bazunu signed a four-year contract at Manchester City in 2020 but is said to have been in talks over his future with Ederson only 28 and tied down to 2026 in the City net.
The Irish Independent report he will either go out on loan again next season, or move on a permanent deal with a number of Premier League clubs interested.
But it is Saints' interest that is reported as strongest, with a solution needed this summer as 34-year-old Fraser Forster approaches the final month of his contract.
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