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The 28-year-old England international has undergone a career resurgence after he signed on loan for West Ham in January.
But Lingard's long-term future at United remains in doubt as his current contract will expire in 2022.
West Ham manager David Moyes is an admirer of the United loanee and is keen to make his switch to the London Stadium permanent.
However, Lingard's £100,000-a-week wage demands could prove to be a major stumbling block to push ahead with the deal.
United could snub a deal with West Ham and use Lingard in their pursuit of Sancho, according to The Sun.
Dortmund are reportedly keeping a close watch on Lingard and would be keen to sign him if they lose Sancho in the summer.
United were heavily linked with Sancho last summer and he has been a top transfer target for Red Devils boss Ole Gunnar Solskjaer.
The Sun reports that Dortmund are holding out on a £100m fee for the 21-year-old English star, though the price could be dropped down with Lingard's inclusion in the deal.
Dortmund's high fee for Sancho would cover the financial loss from the deal as a result of Manchester City's sell-on clause.
The newly-crowned Premier League champions could receive a hefty £16m from the Sancho deal after inserting the clause during his 2017 move to Germany.
United believe that Lingard is worth around £20m, despite his current contract coming to an end next summer.
Dortmund are continuing to push for a top-four spot and securing Champions League football next season amid intense transfer speculation surrounding Sancho and Erling Haaland.
Sancho has cast doubt over his future at the German club after openly admitting that he is unsure if he will be at Dortmund next season.
Speaking after Dortmund's 3-2 win over RB Leipzig last weekend, the England international said: "Will I leave the club? I don't know about my future.
"I am very happy here in Dortmund at the moment. I love the club, the fans and the team. They gave me my first professional start."
Featured Image Credit: PA
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