Ole Gunnar Solskjaer's side continue to be linked with the 20-year-old, who has scored 20 times and contributed 20 assists in 39 appearances for his Bundesliga outfit during the 2019-20 campaign.
BVB are believed to value the England international in excess of £100m, though, which could prove problematic in the current market.
A report has claimed that the Red Devils could instead attempt to agree a swap deal for the former Manchester City youngster, and with that in mind, Sports Mole looks at five players Solskjaer's team could look to include in the proposed deal.
There is no getting away from the fact that it has been a tough season for Lingard, who has contributed just two goals and two assists in 35 appearances in all competitions.
There has been speculation surrounding the attacker's future in recent weeks, and he could well provide an interesting option for BVB.
Indeed, the England international certainly has the pace and movement to be a success in the Bundesliga, and a change of scenery could be just what is needed for the 27-year-old, who is still capable of performing at a high level despite struggling with confidence during the current season.
Dortmund look set to lose on-loan Real Madrid defender Achraf Hakimi this summer, which would open up a spot on the right for a potential new signing.
Dalot has been restricted to just 10 appearances this season due to injury, while he is behind Aaron Wan-Bissaka in the pecking order at Old Trafford.
The 21-year-old is a big talent and could develop into a first-class full-back, but it is likely that United would be prepared to sell the Portuguese if it meant Sancho arriving at the club during this summer's transfer window. In many ways, Dalot would be an ideal replacement for Hakimi.
Smalling was deemed surplus to requirements at Old Trafford last summer following the big-money arrival of Harry Maguire, with the former Fulham youngster joining Roma on loan for the 2019-20 campaign.
The 30-year-old has excelled with the Italian outfit, making 28 appearances in all competitions, developing into an important player for the club in the process.
As it stands, Smalling is due to return to United this summer, but the centre-back is allegedly available for purchase, and Dortmund could do a lot worse than look to the Englishman to boost their defensive unit for the 2020-21 season.
David de Gea
Including De Gea would certainly be a surprise, but a recent report claimed that United would be open to allowing the Spain international to leave for the right price this summer due to his struggles over the last 12 months.
The 29-year-old is still one of the best goalkeepers in world football in full flow, but he has made some mistakes over the last season or so, while United seemingly have a ready-made replacement in Dean Henderson.
BVB could soon be in the market for a new stopper as Roman Burki heads for the final 12 months of his contract, and a very interesting conversation could take place should the German outfit signal that they would be prepared to discuss a potential swap for the former Atletico Madrid youngster.
A recent report has claimed that Sanchez will not be a part of any conversations involving Sancho and a possible swap during this summer's transfer window.
However, it would certainly not be a surprise to see the situation change in the coming weeks, particularly if the Chile international enjoys a strong end to the season for loan club Inter Milan.
Sanchez has only scored five times in 45 appearances for the Red Devils, but there is no question that there is still a wonderful player in there somewhere. Much like Lingard, a permanent switch to a new club could be what is needed for the 31-year-old, who could thrive playing alongside Erling Braut Haaland.