The 28-year-old England international, who is understood to have been at Everton’s Finch Farm training ground on Tuesday, is set to become the club’s second signing of the January transfer window.
The Toffees have already added to their attack this month by bringing in Turkey striker Cenk Tosun from Besiktas for a reported fee of £27million.
Reports have put the fee being paid for Walcott at £20million.
Walcott is surplus to requirements at Arsenal having made just 16 appearances in all competitions this season, including the Community Shield.
Only six of those appearances have been in the Premier League, and he last started a game in the division in April.
Walcott has scored 108 goals in 397 matches for Arsenal in total since joining them from Southampton in 2006.
Tosun made his Everton debut at the weekend, playing an hour of the 4-0 defeat to Tottenham at Wembley.
Speaking last Friday, Everton boss Sam Allardyce said: “Theo’s not as risky (as Tosun) because he’s proven. He’s scored 100 goals for Arsenal from wide positions as well as many assists.
“His pace is one of his key strengths which we lack in this squad. His assists are pretty good as well as his goals.
“We are short of goals so to add power in our goal scoring ability would be very important for me.”