The Saints are expecting an exodus of players and a massive squad overhaul this summer following their relegation from the Premier League.
Armstrong is one of the players who could be heading to the exit door in the upcoming transfer window.
The 26-year-old is rated highly in the Championship and left Blackburn to join the Saints in 2021 to test himself in the Premier League.
Blackburn could try and re-sign him this summer, but that is tipped to be unlikely.
It has been claimed that the forward could be beyond Blackburn’s financial reach in the upcoming transfer window.
Armstrong netted 64 times in 160 appearances for Blackburn during his first stint at the club and could be a potent weapon for the new Saints boss.
If he remains at St Mary’s then he could come face to face with his former club Blackburn in the Championship.