Lingard is set to leave Manchester United when his contract expires at the end of June. Sources have told ESPN that West Ham made contact with the 29-year-old's representatives following the conclusion of the Premier League season on Sunday and negotiations are now under way.
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Sources have told ESPN that Newcastle, who were keen to land Lingard on loan in January, have distanced themselves from a move this summer and are instead focusing on other targets.
Lingard is one of David Moyes' top targets at West Ham this summer after an impressive loan spell at the London Stadium during the second half of the 2020-21 season, scoring nine goals in 16 games to help West Ham to a sixth-place finish in the Premier League.
His form also earned a recall to the England squad and he was named in Gareth Southgate's provisional group for Euro 2020.
Lingard has missed out on a place in the latest squad after a frustrating season at Man United but sources have told ESPN he is hopeful that a run of regular first-team football at the start of next season will be enough to force his way back in ahead of the 2022 World Cup, which starts in Qatar in November.
Lingard played a key role for Southgate during England's run to the World Cup semifinals in 2018.
Sources have told ESPN that new Man United manager Erik ten Hag is keen to speak to the players, including those entering the final weeks of their contracts, but Lingard, who is on holiday in Los Angeles, has already decided it is the right time to move on.
He was restricted to just four starts in all competitions last season and was not included in Ralf Rangnick's squad for the final game of the season, a 1-0 defeat at Crystal Palace.