Lingard is available on a free transfer after he left Manchester United at the end of his contract this summer.
The 29-year-old has offers from MLS and Saudi Arabia, but he is now expected to stay in the Premier League next season and it has been suggested he wants to be at his next club by Friday.
A decision over his future is expected this week and the race is down to two Premier League clubs, Nottingham Forest and West Ham.
And it has been claimed that the East Midlands club are increasingly confident about their chances of signing Lingard on a free transfer.
Negotiations are ongoing between Forest and Lingard’s representatives and the newly-promoted side have offered him a two-year deal.
The two sides have an agreement over his wages but a deal has not been finalised yet as Lingard still ponders over his next move.
He has an offer from West Ham where he had a good loan spell last year but the Hammers have refused to bow down to his wage demands.
There are suggestions that Forest’s offer is more lucrative to the one he has received from West Ham.
Steven Cooper’s side are currently leading the chase to sign the attacking midfielder on a free transfer.