Walcott’s old club are first in the queue to take the former England forward out of the Emirates during the January transfer window, but both Everton and Newcastle are also keen.
Saints want to negotiate a loan move, who they sold to Arsenal as a 16-year-old 12 years ago, but West Ham are now considering a similar bid as new manager David Moyes reshapes his squad.
Walcott still has a year left on his £120,000-a-week Arsenal contract, but there is general acceptance a move would be in his best interests now.
The forward is yet to start a league game this season, and has made only four substitute appearances, with all eight of his starts coming in either the Carabao Cup or the Europa League.
Walcott desperately wants first-team football and Saints, whose results have nosedived over the festive period, would look to make the move a permanent one in the summer.
They are only outside the relegation zone on goal difference after extending their winless run to nine games by losing 2-1 at home to Crystal Palace on Tuesday.
Fans are calling for Mauricio Pellegrino to be sacked just seven months after the Argentine replaced the axed Claude Puel but Shane Long, who ended an 11-month goal drought to put Saints ahead before they collapsed in the second half, said: “We know it is frustrating for the fans but we do need them now more than ever.
“It’s on the players’ heads as well. We practise well all week. We cannot put it on the manager’s head – everyone has to take a bit of the blame.
“We have got a lot of good players in the squad and a lot of players who deserve to be in the starting 11. I am sure in the future it will come good.
“I have experienced this before and so have a few other lads. We just need to pick ourselves up. Confidence is low at the moment and the sooner the win comes the better.
“When we went 1-0 up we were playing well and contained them. But in the second half they came at us. Naturally you drop off and try and hold onto your lead and that cost us.
“If you are high up the table we would just have kicked on and got three or four goals but it was in the back of our heads we needed a win and we invited them onto us.”
Despite their dismal run of form, Saints are reluctant to give Pellegrino the boot.
The former Liverpool defender has been promised funds to spend this month from Virgil van Dijk’s £75m move to Liverpool.
Arsenal outcast and ex-Saint Theo Walcott is Pellegrino’s top target and is close to agreeing a loan move back to the south coast.
Saints chairman Ralph Krueger has given his backing to Pellegrino, saying: “In no way shape or form am I angry at any one individual for what has happened here in the past months.
“We believe we can climb back up the table with the group we have. We’re a club on a long-term plan.
“From the get-go, Mauricio has completely embraced the way we operate here. The transfer that has just gone through is the end of a very difficult phase for the club.
“We feel we have a superb group of players at the club and that we’re well poised to attack the second half of the season.”