The Gunners forward has played just 47 minutes in the Premier League this season and is yet to start a league game after being mainly used in the cup competitions. Walcott has been silent with regards to his future, but is likely to want to play more regularly to give himself a chance to make Gareth Southgate's World Cup squad.
Arsene Wenger has maintained that the England international remains in his plans for the current campaign and the manager will be reluctant to allow an experienced first-team player to leave midway through the campaign.
According to the Mirror, however, Wenger could consider a loan move for the striker as he is aware of the player's frustration owing to the lack of game time this campaign. Southampton are said to be leading the race, but will face competition from Everton and West Ham if he is made available for a transfer in January.
Walcott is Arsenal's longest serving player and despite the striker falling behind Alexandre Lacazette, Olivier Giroud, Danny Welbeck and Alexis Sanchez in the pecking order, he was the Gunners' second highest scorer last season with 19 goals in all competitions.
All three teams are looking to bolster their attack and Walcott will be high on their list if made available. According to the Telegraph, interested teams will not be able to pay the striker his current wages, which stands at £120,000-a-week, but believe a compromise can be reached.
The report also says that even Arsenal believe his departure is imminent either in January or during the summer, when he will enter the final year of his contract with the club. The Saints will be installed as favourites as Walcott came through their academy before joining Arsenal as a 16-year-old in 2006.