Everton's offer is expected to fend off rivals, including Southampton.
Walcott is yet to start a Premier League game this season, having fallen behind Alex Iwobi and Danny Welbeck at Arsenal, but could well make his debut for Everton against West Bromwich Albion at Goodison Park on Saturday.
The winger will be hoping that a move to Everton will kick start his career, and be able to earn himself a place in Gareth Southgates squad for next summers World Cup in Russian Federation.
The 28-year old came off the bench in the Gunners' 2-1 loss to Bournemouth at the Vitality Stadium this past weekend, and that could very well turn out to be the last time Walcott dons the Arsenal colours.
The Saints had also been keen to land the England global but it appears Everton have now won the race for the 28-year-old's signature.
The North Londoners are also hoping to sign Manchester United midfielder Henrikh Mkhitaryan in a deal which would involve Alexis Sanchez going the other way after previous suitors Manchester City dropped out of the running.
Giroud could be involved in a deal to bring Pierre-Emerick Aubameyang to the Emirates this month.
Kylie Jenner Not in Labor With First Child Despite Rumors
The source added that Jenner deserves to keep her pregnancy to herself because she already grew up in front of the cameras. The source revealed: "She wants to be in her own house with the baby and Travis".