The 33-year-old has struggled for game time under Ralph Hasenhuttl this season, featuring in only 12 games across all competitions this season, with his last outing back in February in the FA Cup.
As Walcott is approaching the final year of his contract at St Mary's, The Sun claims that he is considering a switch to the USA, with a move to either Los Angeles or New York believed to be his preferred destination.
After beginning his career on the South Coast back in 2005, Walcott eventually returned to the Saints on a season-long loan deal from Everton for the 2020-21 campaign.
The former Arsenal man then made his temporary deal permanent last summer, but he has since become a peripheral figure, with the likes of Mohamed Elyounoussi, Stuart Armstrong, Nathan Redmond and Nathan Tella all preferred ahead on him on the flanks.
The futures of Southampton quintet Alex McCarthy, Fraser Forster, Willy Caballero, Jack Stephens and Shane Long are also uncertain as they will all see their contracts expire next month.