Wilshere is out of contract at the Emirates at the end of the season, and is set to sign a new deal, fuelling speculation he could be on his way out of North London having fallen out of favour with manager Arsene Wenger.
The Englishman was shipped out on-loan to Bournemouth last season, however after returning to Arsenal in the summer has failed to establish himself as a regular in the first-team.
Hammers manager David Moyes has admitted his interest in Wilshere already, and Wilkins believes that the midfielder would be a solid signing for the club.
The pundit said on TalkSPORT: “I think 25 years of age, I don’t know how much you’d have to pay, but because Arsene doesn’t play him, he needs to move. I’d love to see him play, because I think he could get to the World Cup. I’d snap him up all day long, I really would.
“London guy, his family are West Ham supporters, why not go to West Ham? David Moyes has them rocking at the moment.”