HULL City are confident they will hang onto Steve Bruce - even if Saints decide Ronald Koeman is not the man to replace Mauricio Pochettino.
There has been speculation Bruce is interesting Saints, though Duch legend Koeman remains the red hot favourite.
Bruce's superb spell at the Tigers includes leading them to promotion from the Championship in 2012/13, and the club's first ever FA Cup final last season.
Hull also confounded their critics by comfortably avoiding relegation, though they were twice beaten by Saints - 4-1 at St Mary's and 1-0 at The KC Stadium.
Saints right back Calum Chambers, meanwhile, remains linked with a move to Arsenal.
According to reports, Arsene Wenger - no stranger to raiding St Mary's for Saints academy graduates - sees the England under-19 skipper as a potential replacement for Bacary Sagna.
The Frenchman could be on his way to join Manchester City on a Bosman.