The England international has featured in eight Premier League games for the Hammers since his loan move in January, and he has bagged a goal or assist in seven of them during an unforeseen turnaround in fortunes.
Lingard's agreement with West Ham is a straight loan without an option or obligation to buy, but the club are understandably keen to keep him at the London Stadium on a permanent basis.
A senior West Ham source told Sky Sports News: "We will do whatever it takes to sign him. He has been outstanding for us."
The Manchester United loanee boasts a total of six goals and four assists from eight top-flight appearances for David Moyes's side, and he is playing a starring role in their bid for a Champions League place.