With the Hammers sitting in the Premier League relegation zone, Moyes will be active at the start of 2018 and the East London outfit have been linked with a move for Wilshere.
The playmaker has featured for just 86 minutes in the top flight this season, and with the England international having just over six months remaining on his contract, Moyes has hinted at interest in the player's signature.
The Scot told reporters: "You'd hope that if you took a player from another Premier League club it'd be much easier for him to go right into the team and play well. Jack Wilshere would be someone who we'd have to look at if he was available.
"I do believe the transfer window could be the difference between relegation and staying up. If we can get the right players, that's the big part of it."
West Ham play host to Arsenal at the London Stadium on Wednesday night.