The Gunners want to raise funds and are preparing for a January clear out at the Emirates.
Mesut Ozil is also in line to be sold with his contract expiring next summer.
And while Walcott’s current deal runs until 2019, Arsenal have no intention of extending it.
Arsene Wenger wants to reshape his side and Walcott is not in his future plans, having struggled for game time this season.
According to the Daily Express, Southampton would pay between £12m and £15m for the 28-year-old.
Mauricio Pellegrino’s side have struggled for goals and Walcott would bolster their frontline for the second half of the campaign.
The Arsenal winger, who has scored 107 times for the club since leaving Southampton in 2006, still has a soft spot for his old side.
With England having now qualified for the World Cup in Russia next year, Walcott needs game time to get himself in contention for a place on the plane.
However, the Daily Express add Southampton are not the only club interested.
Everton and West Ham are said to be admirers of Walcott, with Inter Milan also eyeing the Arsenal ace.
Ronald Koeman and Slaven Bilic’s teams have both been surprise early strugglers.
Walcott would offer pace and experience to either the Toffees of the Hammers.
But it is Southampton who appear most inclined to end his Arsenal career and take him back to St Mary’s.
