Todd noted how new Toffees manager Sam Allardyce is keen to add Walcott's pace to his squad as the Merseyside club is still searching for an adequate replacement for Romelu Lukaku.
The Belgium international left Everton to join Manchester United in the summer, and the failure to replace him doomed the tenure of Ronald Koeman, who was fired in October.
The Dutchman left with the Toffees in the bottom three and had ironically spent most of the summer trying to sign another Arsenal striker, Olivier Giroud.
Everton couldn't get a deal over the line for Giroud but may have more success pursuing Walcott. The attacker has recently been told by manager Arsene Wenger he can leave the Gunners in January, according to Daniel Cutts of The Sun.
It's hardly a surprise exit rumours involving Walcott are growing since he's made just six starts this season, all outside the Premier League. Instead, Wenger has trusted summer signing Alexandre Lacazette, Danny Welbeck, Giroud, Alexis Sanchez and Alex Iwobi along the forward line.
An inability to produce goals and assists consistently, along with not having an obvious place in Arsenal's 3-4-2-1 formation, has led to Walcott's declining status in north London, per ESPN FC's Tom Adams.
Walcott's patchy form, as well as his struggles avoiding injury, are a shame since his pace and finishing ability can make him useful for any team.
The 28-year-old's movement and composure in front of goal have improved since he joined the Gunners in 2006, but he still lacks the strength to play with his back to goal and the technical accomplishment to link well with others.
Arsenal have enough depth in attacking areas to let Walcott try to make the grade elsewhere, even if it means selling him to a rival.
Getting a fee for a player on the fringes of his squad and using it to reinforce threadbare options in central midfield would be smart business from Wenger in January.