Manchester United have told Lingard he can leave this month and David Moyes is interested in taking the midfielder to West Ham on a deal until the end of the season.
But Premier League clubs are only allowed two domestic loan players in their squad and West Ham have already borrowed Benrahma from Brentford and Craig Dawson from Watford.
West Ham have an agreement with Brentford to sign Benrahma for £20m plus £5m in add-ons at the end of the season but they plan to bring that forward to sign Lingard.
Moyes knows Lingard from his time in charge at Manchester United and the 28-year-old, who has made just three appearances under Ole Gunnar Solskjaer this season, needs to reignite his career.
West Ham are also keen to sign a striker after selling Sebastien Haller to Ajax for £20m. They have shown an interest in Bournemouth’s Joshua King and Reims forward Boulaye Dia, while RB Leipzig’s Hwang Hee-chan is also among their possible targets.
Moyes has revealed he wants to sign two players this month in a bid to ensure their good work in the first half of the season is not scuppered by a lack of depth.
West Ham can move into the Champions League places if they beat Crystal Palace at Selhurst Park tonight and Moyes said: “We’re in a strong position and I want us to remain in a strong position if we can.
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“If I can get another player in then great, another two even better. I want us to stay competing and being competitive between now and the end of the season.
“We’ve certainly got cover with central defenders at the moment and full-backs who can play if required. Mark Noble again was probably the best player on the pitch [against Doncaster on Saturday].
“We’re quite strong but I want to make sure we’ve got enough creativity and enough people who can score me the goals and make the difference at the top end of the pitch when needed. If I see the right players around and I can get them I’ll try and do so.
“We’ve got some positions where we’re light. We let Snoddy [Robert Snodgrass] go and we let Seb go, we’ve lost two senior players there. I’m feeling that we’re light but we introduced some younger players. We’re also very aware that it wouldn’t take much, a couple of injuries, and we might need to start looking elsewhere.
“The owners are very supportive in backing me with what I choose to do but I what I am trying to do is choose correctly for the team. Whether it be a loan or permanent, I can’t guarantee but I am trying to add.”