The England international has been tipped with a move away from the Emirates Stadium in order to find more regular game time ahead of next year’s World Cup finals.
And speaking ahead of this evening’s Premier League clash against the Gunners, newly appointed Hammers boss Moyes - who oversaw the defeat of another London rival in Chelsea last weekend - would be keen to have Wilshere as part of his plans for the rest of the season and potentially beyond.
"Jack Wilshere would be someone who we'd have to look at if he was available,” said the former Manchester United and Real Sociedad boss.
"I also want to make sure we're looking at players who can be at the club for a long period and not just in for a short period.
"Then there's also the short-term fix for me which is how do we get enough wins between now and the end of the season? There's a balance between that.”