The 28 year old England hopeful spent this season on loan at Newcastle United and made 23 appearances, including four in the Champions League.
The Magpies paid approximately £4million to St Mary's to loan him for the season, as well as covering his huge wages, following the club's relegation.
They have an option to buy Ramsdale permanently, but it is not clear whether they will take that up this summer, or look elsewhere to replace Nick Pope.
The Athletic report that there will be significant interest in him, both from mid-table Premier League clubs and continental-qualified teams in Europe.
Saints paid £18m to buy Ramsdale from Arsenal in 2024, with a further £7m payable in add-ons. At least £1m was linked to Premier League survival.
Saints are likely to be keen on moving Ramsdale on once again after they were denied winning promotion from the Championship due to Spygate.
They qualified for the play-off final and were one game away from a £115m broadcast revenue windfall before they were expelled from the competition.
It follows midfielders Shea Charles and Caspar Jander also being linked with moves away, with Man United and German clubs interested respectively.