But former West Ham United defender Glen Johnson believes the club will pip his former team to his signature in the summer, when the forward will be a free agent.
Deadline day talks over a loan move for Lingard came to nothing, despite Manchester United interim manager Ralf Rangnick’s willingness to farm out the 29-year-old in the final few months of his Old Trafford contract.
The England international spent the second half of last season on loan at West Ham, and the assumption in some quarters has been that he would favour a return to the London Stadium at the end of the campaign.
However, Johnson believes that relegation-threatened Newcastle, “poised” ahead of the summer transfer window, will have the edge in talks – if they stay up this season.
Speaking to bettingodds.com, Johnson said: “It doesn’t look like a move to West Ham is going to happen. Since he went back to Manchester United, it never looked like a move was going to happen.
"The player never said he wanted to go, his club didn’t say they wanted him to go. If the player really wanted to go, then it would have happened by now. I don’t think it’s going to happen.
"His contract is expiring and Newcastle are sitting poised, waiting to offer him something, so I can’t see him ending up at West Ham now.”
Newcastle head coach Eddie Howe was asked about Newcastle's attempts to sign Lingard – who scored nine goals for West Ham last season – earlier this month.
"Jesse Lingard’s a player I have always admired – and that's probably the best thing to say,” said Howe, who signed five players last month, including Lingard’s England team-mate Kieran Trippier.
Meanwhile, Newcastle take on fifth-placed West Ham, pushing for a Champions League place, at the London Stadium on Saturday.
Howe’s 17th-placed side, unbeaten in five games, are four points above the Premier League relegation zone following three successive victories.
"We've worked incredibly hard," added Howe. "In the last three games, I don't think there's been any secret to how we've won the games.”