Lingard enjoyed a sensational loan spell at the Hammers after arriving in the January transfer window.
In total, he made 16 Premier League appearances and scored nine goals, while also laying on five assists.
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His form was so good that Gareth Southgate included him in his provisional England squad of 33 players prior to Euro 2020, though he was cut when it was reduced to 26 players.
Reports have suggested that the Hammers will make a serious attempt to bring the playmaker back to the club on a permanent basis this summer, though conflicting stories have also claimed that he may want to stay at Old Trafford, with ExWHUemployee claiming he could even sign a new contract, via Football FanCast.
Fry doubts the latter claims, though, and believes that he will want to stick around in east London.
Speaking exclusively to This Is Futbol, Fry, who knows senior Hammers figures well, said: “I think they’ll be after Lingard and quite rightly so, he’s had a big impact on the team. He never got a look-in at Man United so Moyes has done him proud to bring him in and he’s played him from the start, which is absolutely amazing, because he hadn’t had any game time at all at Man United but of course, Moyes was at Man United so he knew the boy personally.
“The boy has come and played and Moyes just said ‘go out there and enjoy yourself’. He had a lot of faith in him and Lingard has repaid that faith by putting in some outstanding performances. Jesse Lingard will want to play and he isn’t going to play at Man United.
“He’s got one year left next year, he won’t be interested in whatever they offer him, he’ll want to play and I think Moyes will be top of the list, he’ll want to join Moyesie because he knows he’ll play and he gets the best out of him.
“It’s just whether they can come up with the numbers that Man United will require.”