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The 28-year-old has struggled for regular playing time this term and he has yet to make a single appearance in the Premier League campaign.
Inter Milan have been credited with an interest in his services, but Sky Sports claims that Nice are also in the running to land him.
Lingard's agent has been in talks with the French outfit and there could be an official approach from Adrian Ursea's side next week.
Lingard's contract was initially due to expire at the end of the campaign, but United triggered a 12-month extension clause.
The attacker has been largely out of contention under since the arrival of last winter.
Lingard has made the matchday squad in just four Premier League matches this season.
The Red Devils are currently top of the table with a three-point lead over rivals Liverpool, whom they face on the road this weekend.
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