Lingard is expected to make a decision over his future this week as he takes a call on which club to join.
He is available on a free transfer after he left Manchester United in the summer and has already rejected offers to move to the MLS and Saudi Arabia.
The race is down to West Ham and Nottingham Forest with the Hammers reportedly growing pessimistic about their chances of signing him.
But it has been claimed that West Ham are happy with the offer they have put forward to Lingard and are unlikely to improve it.
The east London club are now waiting for an answer from the 29-year-old, who had a brilliant loan spell at West Ham in the latter half of the 2020/21 season.
David Moyes is keen to reunite with Lingard but the club have been reluctant to meet Lingard’s wage demands of around £180,000 per week.
Nottingham Forest have also made a substantial contract bid with suggestions that they have offered more money than West Ham.
The newly-promoted Premier League outfit are said to be ready to break their wage structure to land Lingard.
