The attacker has now officially become a free agent, with his contract at Manchester United expiring at the end of June, and the Hammers are in the mix for his signature.
According to Sky Sports News, David Moyes's side have made 'a good offer' to the England international, but the player is yet to signal whether he is prepared to accept the deal on the table.
Lingard starred on loan at the Hammers in the second half of the 2020-21 campaign, and Everton and Tottenham Hotspur are both believed to be in the mix for his signature at this stage.
Meanwhile, according to Football Insider, Andre Gray is set to join Greek side Aris Thessaloniki FC on a free transfer following his release from Watford.
The 31-year-old enjoyed a productive campaign on loan at Queens Park Rangers during the 2021-22 campaign, finding the back of the net on 10 occasions in 28 Championship appearances.
Watford decided against renewing the forward's contract, with the forward leaving on a free transfer, and it is understood that he is preparing to make the move to Greece.
A number of clubs are said to be have been in the mix for his signature, but a switch to Aris would see him play in the Europa Conference League next term.
Elsewhere, Nottingham Forest are reportedly planning a bid for Huddersfield Town left-back Harry Toffolo, with the Reds preparing for life back in the top flight of English football.
Toffolo only has one year left to run on his contract at Huddersfield, and the 26-year-old is believed to be on the radar of a number of clubs during the summer transfer window.
According to The Athletic, Forest are preparing a bid for Toffolo, who made 48 appearances at club level during the 2021-22 campaign, contributing six goals and eight assists in the process.
Forest are also pressing ahead with a move for Liverpool defender Neco Williams, who has seen a potential move to Fulham break down.
Meanwhile, according to 1908.nl, Man United attacker Tahith Chong is in talks with Feyenoord over a return to the Dutch club this summer.
The 22-year-old is back at Old Trafford after a loan spell at Birmingham City, with the attacker currently involved in pre-season training for the Red Devils.
However, he is not believed to be in the plans of Red Devils boss Erik ten Hag moving forward, and Feyenoord are said to be in discussions over a move for the Dutchman.
Chong initially moved to Man United from Feyenoord in 2016, but he has only made 16 first-team appearances for the 20-time English champions during his time at the club, spending time out on loan with Werder Bremen, Club Brugge and Birmingham.