According to Tony Banks in the Express, Arsenal have no plans to renew Walcott's current contract—which expires in 2019—and Saints will look to offer between £12 million and £15 million to re-sign the 28-year-old.
Walcott signed for Arsenal from Southampton in a deal worth up to £12 million back in January 2006, when he was just 16.
He had showed huge potential at Saints and arrived at Arsenal amid much excitement and expectation.
Despite making almost 400 appearances for the Gunners and winning three FA Cups, Walcott has never quite lived up to his early potential.
By some distance his most productive season was back in 2012-13, when he netted 14 goals and provided 10 assists in 32 Premier League appearances, per WhoScored.com.
After the summer addition of Alexandre Lacazette, the ongoing emergence of Alex Iwobi and return to fitness of Danny Welbeck, Walcott has barely been used by manager Arsene Wenger in 2017-18—he has played 47 minutes in the English top flight.
Back at Southampton he could be valuable, though. The south-coast club lack any real attacking verve and have netted only five goals in seven league matches so far this term.
Walcott still boasts great pace and dynamism, while his experience could make him a brilliant addition to Mauricio Pellegrino's squad at St Mary's.
Given that he looks set to remain on the fringes at Arsenal, a move to Saints for Walcott in the January transfer window could work in favour of all parties involved.