Saints boss Russell Martin is shaping his squad for a season of Championship football and he could lose a number of players in the aftermath of relegation.
Proven Premier League hitman Adams is drawing attention with both Crystal Palace and Fulham interested in taking him to the capital.
And it is claimed that though no move for Adams away from St Mary’s is advanced, interest in him is growing.
It is suggested that if Southampton do cash in on Adams then they would be likely to be able to bank a fee in the region of £15m.
Crystal Palace are keen to add to their firepower this summer, while Fulham could yet lose the services of Aleksandar Mitrovic, who has a lucrative offer from Saudi Arabia on his table.
Saints captured Adams from Birmingham City in the summer of 2019 for a sum in the region of £15m.
He regularly chipped in with goals in the Premier League for the south coast club and they may lose his nose for goal this summer.
