The English midfielder's future at the north London club remains uncertain as Arsenal are yet to offer him a new deal despite Wilshere being close to entering the final six months of his contract. He will be free to talk to clubs outside England from January.
The 25-year-old is keen to remain at the Emirates and fight for his place under Arsene Wenger but is aware that the lack of regular Premier League football will jeopardize his chances of booking a place in Gareth Southgate's 23-man squad for next summer's World Cup in Russia.
Wilshere has been a regular in the Europa League and the Carabao Cup but has been limited to substitute appearances in the league thus far. But he could start when Arsenal take on West Ham United on Wednesday (13 December) at the London Stadium owing to Aaron Ramsey's injury.
Moyes is looking for reinforcements during the January transfer window and would be interested if Wilshere is allowed to leave. The former Everton manager also believes that January additions are needed to help the Hammers get out of the relegation battle – they are currently in 19th place with 13-points.
"Jack Wilshere would be someone who we'd have to look at if he was available," Moyes said ahead of West Ham's clash against Arsenal, as quoted by Sky Sports. "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.
"That's why those decisions will have to be mutually taken with [head of recruitment] Tony Henry, the chairman and myself to make the right deals," the former Everton boss explained. "I've got an idea of where I need to strengthen. We've already said there's a little bit of an imbalance but that can happen at football clubs."
"Could January be the difference between staying up and going down? I do believe it could. I think if the right players are available we should try and do something. If we can get the right players, that's the big part of it."
The West Ham manager also indicated that they could be interested in a move for Olivier Giroud, who admitted recently that he could leave in January if the right opportunity arose after struggling for game time in the Premier League.
The French striker is also keen to play regularly to maintain his place in the France squad for the World Cup, and the Hammers, who were interested in the summer, could return, as they look to bolster their attack. However, Arsene Wenger has ruled out the possibility of letting the striker leave midway through the campaign.
"We've got a lot of strikers so I think for us to be linked to strikers at the moment might not necessarily be the right thing," Moyes said about signing a striker.
"But who knows? I think Olivier Giroud is a talented footballer and has a record of scoring goals."