The 28-year-old has lost his spot in the England squad under Gareth Southgate, despite finding the back of the net on 19 occasions for his club during the 2016-17 campaign.
Walcott also started 23 of Arsenal's 38 Premier League fixtures last term, but a switch to a 3-5-2 formation in the latter stages of the season saw the former Southampton youngster spend time on the bench.
According to The Mirror, Walcott is desperate to secure first-team football for the 2017-18 campaign as he bids to make the England squad for the 2018 World Cup, and West Ham will offer the forward the chance to become a key player at the London Stadium.
The report claims that the Hammers feel a bid in the region of £25m would be enough to convince Arsenal to sell.
Walcott has scored 104 goals in 377 appearances for Arsenal following a 2006 move from Southampton.