According to Adrian Kajumba of the Daily Mirror, Toffees manager Sam Allardyce is a fan of Walcott and wants to give him the chance to ignite what has been a disappointing term for him so far. The England international is yet to start in the Premier League in 2017-18.
Kajumba reported Everton have intensified their interest in Walcott by making an enquiry for the 28-year-old.
Additionally, Everton are also set to pip the Gunners and West Ham United to the capture of N'Zonzi, who has been marginalised at Sevilla. The Toffees will reportedly sign the Frenchman on loan in January until the end of the campaign with a view to a permanent switch in the summer.
Walcott is someone who looks as though he would benefit from a move at this point in his career, as opportunities have dried up at Arsenal.
When he has been given a chance, though, the forward has shown some signs of promise, as noted by Fox Sports' Keith Costigan:
While Alexandre Lacazette, Alexis Sanchez and Mesut Ozil are the front three preferred by manager Arsene Wenger—with Olivier Giroud, Alex Iwobi and Danny Welbeck used as back-up—it's worth remembering Walcott netted 19 goals last season.
In the right type of setup, it's clear the former Southampton man still has something to offer. His blistering speed still causes problems for defenders, and while his decision-making in other areas of the field lets him down on occasion, in front of goal he's a reliable finisher.
Still, as Bleacher Report's James McNicholas noted, Walcott is a little too limited to be starting on a regular basis for the Gunners:
As for N'Zonzi, if he were to arrive at Arsenal and reach the levels we have seen for Sevilla over the past couple of seasons, he would be a fine capture.
The Frenchman was colossal for the Andalusians prior to this campaign. Sitting in front of the back four, his ability to break up play, carry the ball forward and distribute with intelligence made him stand out as one of the best midfielders in La Liga.
This term, however, he's fallen out with manager Eduardo Berizzo and hasn't started a game since the memorable 3-3 draw against Liverpool in the Champions League on November 21.
These numbers from WhoScored.com suggest the 29-year-old may be more suited to Allardyce's brand of football:
Arsenal have lacked defensive nous and power in the centre of midfield for a long time now. However, given his age and the manner in which matters have turned sour at Sevilla, perhaps it's understandable Wenger would be hesitant about this one.
As for Walcott, the time has surely come for him to take on a fresh challenge having joined the club in 2006. At Everton he'd get regular football and a chance to relaunch a career in danger of fizzling out. Arsenal surely wouldn't begrudge him that switch if the opportunity was to present itself.