The former Manchester United midfielder is also considering a lucrative offer from Abu Dhabi but a move to MLS has been ruled out, sources added. Lingard also has an offer on the table from a club in Saudi Arabia and a final decision about his next move is expected before Friday.
The 29-year-old is a free agent after officially leaving Old Trafford following the expiration of his contract at the end of June. He has been training alone during the summer break and will join up with his new club on the completion of the deal.
Lingard left United after struggling for opportunities last season. He is keen for regular first team football at his next club and still hopes to force his way back into the England squad ahead of the World Cup, which starts in Qatar in November.
West Ham are keen to sign Lingard after a successful loan spell at the London Stadium at the end of the 2020-21 season, said the sources. He scored nine goals in 16 games for David Moyes' side to earn a place in England's preliminary squad ahead of the European Championships, but West Ham face competition from Premier League rivals Everton and Tottenham.
Everton manager Frank Lampard is looking to rebuild his squad at Goodison Park after flirting with relegation last season and is keen to bring in Lingard.
Tottenham have also expressed their interest, but a move to the Middle East is also still considered to be a possibility.