Walcott has been disappointing for Arsenal this season and is for another challenge after losing his place in the team.
West Ham boss Slaven Bilic according to reports is willing to play the 27-year-old at his preferred striking position.
Bilicwas in charge of Croatia when when Walcott tore their defence apart with a hat-trick for England in a World Cup qualifier in September 2008.
Transfer reports revealed that Hammers are yet to make a formal offer for the player, but Arsenal are bracing themselves for a bid.
West Ham are also interested in Marseille player Michy Batshuayi and Liverpool striker Christian Benteke.
Benteke has fallen out of Liverpool’s starting 11 since Jurgen Klopp took over the club and the Belgian will be interested in a move away from Anfield.
West Ham have kicked off talks with Marseille over a £30million switch for Batshuayi.