Saints are heading for relegation from the Premier League following a series of blunders from owners Sport Republic.
The club have worked their way through Ralph Hasenhuttl and Nathan Jones as managers, with Ruben Selles then placed in charge when a bid to appoint Jesse Marsch collapsed.
Southampton’s owners are expected to launch a massive overhaul of the club when relegation is confirmed.
A number of players are likely to leave St Mary’s, but it is claimed that Bazunu is one they would like to keep hold of.
The goalkeeper is rated as a future gem by owners Sport Republic.
Bazunu, 21, has made 32 appearances for Southampton in the Premier League so far this season, conceding 56 goals and keeping four clean sheets.
Southampton have the shot-stopper locked down on a contract which is due to run until the summer of 2027.
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