Everton boss Sam Allardyce is hoping to persuade Walcott to make the move to Merseyside by stating that he can help resurrect his career, while also offering him an outside chance of making England's World Cup squad.
The 28-year-old has fallen down the pecking order at the Gunners this season having thus far only made five substitute appearances in the Premier League.
"You're all aware in our interest in Theo", Allardyce told a news conference.
He said, "If that is possible to get over the line I would be delighted but obviously there is negotiations that are happening at the moment".
"If we can get that all sorted out then that would be a great addition to join us from an attacking point of view".More news: Dolly Everett farewelled by hundreds of mourners in Katherine
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Since Allardyce was appointed at Goodison Park, the Toffees have scored eight times in as many league games, prompting the former England boss to also snap up Turkey worldwide Cenk Tosun last week in a £28 million deal.
"If that is at all possible it would be very nice. You never get excited until someone has signed on the dotted line", he said. Allardyce also thinks he can give Walcott the chance to make a late run to try to force his way into England's World Cup squad, however unlikely that may now seem. People laugh at us - they see it as a bit of a joke with what's going on at the moment - players don't want to be there.
Everton hope that an offer in the region of £20m will be enough to tempt Wenger into selling, while they are also ready to match Walcott's £110,000-a-week Arsenal wages.
Asked if the move was motivated by Walcott's global ambitions, Wenger said: "Yeah of course, everyone wants to play".
"He went in 2006 and we are now in 2018 and he hasn't been since for different reasons".