Sources have told ESPN that Tottenham have registered their interest in Lingard but are yet to make a formal offer.
Lingard is assessing his options and is set to make a final decision about his future based on where he is most likely to find regular first-team football.
After a successful loan spell at West Ham United last season, he has found opportunities at Old Trafford limited so far this term.
Sources have told ESPN he is keen to win back his place in the England squad ahead of the 2022 World Cup in Qatar after his form at West Ham earned a place in Gareth Southgate's provisional squad for Euro 2020.
Sources have told ESPN that Spurs manager Antonio Conte is pushing the club to strengthen the squad in January but it is more likely any deal to sign Lingard would happen in the summer.
United interim manager Ralf Rangnick is aware that a number of players want to leave but he is keen to keep the majority of his squad players while they remain in the FA Cup and the Champions League.
As well as trying to secure a place in the Premier League's top four, United are through to the fourth round of the FA Cup and face a Champions League round-of-16 tie with Atletico Madrid in February.