Lingard's future prospects at Old Trafford look bleak, even though manager Ole Gunnar Solskjaer said he expects the winger to return to the club.
But Moyes hopes West Ham's climb up to fifth in the Premier League makes them an attractive proposition.
"I hope we're going to be in a position to attract many players in the future, because of our league position, because we're a club with stature, we're in London, we have a 60,000-plus stadium which will be full every week. I think all those things go in our favour," said the Hammers boss.
"Jesse wanted to come here, right from the start. When I was talking to him he wanted to come to West Ham. He saw it as a really good place for him. I think he'll have seen what we're trying to do.
"He's joined a good group of players as well. We've got international players and I'm hoping we can add to that in the coming transfer window. The job is to try to add to that.
"But I would hope Jesse sees this as a good place if it's possible to be done, and if we think that we want to do it at the end of the season."