Ex-Everton boss Roberto Martinez could make a swift return to management.
The report claims that Koeman is in talks with Everton and should he decide to leave the Saints and join the Toffees then Martinez, Bournemouth’s Eddie Howe and Ajax boss Frank De Boer are the three early candidates to potentially replace him.
Martinez received his marching orders from Everton last month following a poor campaign at Goodison Park.
The Spaniard took over the Toffees in the summer of 2013 and guided the club to their best ever Premier League points tally during his debut campaign, yet it ultimately turned out to be a false dawn.
Everton since struggled under his guidance, and this season not even an exciting FA Cup run to the semi-finals could save his job as the club struggled badly towards the back-end of the season.
Koeman has been identified as Everton’s number one target to take over the vacant managerial position at Goodison Park, leaving Southampton in a potentially difficult position.
The Saints boast a talented group of players, yet finding a potential worthy successor to Koeman could be a lengthy process and one which the club will not be able to take lightly.
The report claims Martinez is ironically among those linked, though supporters would probably prefer Ajax boss De Boer or Howe should he be willing to leave south coast rivals Bournemouth.