The 28-year-old hasn't started a Premier League game under Arsene Wenger this season and the Frenchman might well sanction his move if the deal is right.
And one way that Wenger could make the deal a good one is by asking for Everton midfielder Idrissa Gueye in a swap deal for Walcott.
Gueye has not had the best of seasons at Goodison - who has? - but he was brilliant under Ronald Koeman last term and Wenger, according to The Sun, was interested in signing the 28-year-old in the summer.
New Everton boss Sam Allardyce will surely look to shape the squad in his image during January and Gueye is not an archetypal Allardyce midfielder. At 5,7, he is not a Mo Diame, a Cheikhou Kouyate or a Steven N'Zonzi, who they are linked with after the English manager brought him to Blackburn.
He is, however, a player who the Gunners could use in their central midfield, with Granit Xhaka looking less like a £35 million player every time he pulls on the shirt.
The Swiss is by no means a bad footballer, but he does not shield Wenger's often-shaky defence in the way that Gueye would.
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The money from Walcott's prospective sale won't make a huge difference to Arsenal and Wenger should instead ask his old foe if he would be willing to part with the Senegalese midfielder.