The injury-hit Arsenal midfielder is set to play against the Hammers tonight at the London Stadium.
But the England international is in the last year of his contract and has yet to make a single Premier League start this season.
A switch to the Hammers, who are on a high from Saturday’s 1-0 victory over champions Chelsea, could revive Wilshere’s fortunes for both club and country.
And Moyes made it clear he would be interested in signing a man who has been kept ticking over in domestic cup and Europa League action so far this term.
“Jack Wilshere would be someone who we’d have to look at if he was available,” he said.
“I also want to make sure we’re looking at players who’ve got time and who can be at the club for a long period, not just in for a short period.
“This is a window where we need somebody who can hit the ground running. You would hope if you took a player from another Premier League club he would be able to go right into the team and play well.
“Could this window make the difference between staying up and going down? I do believe it could.”