As a result, a recent report has claimed that Erik ten Hag's side have joined the hunt for Lewandowski, who has expressed a desire to leave Bayern this summer, one year before the end of his contract.
Lewandowski again enjoyed an impressive campaign for Bayern in 2021-22, scoring 50 times and registering seven assists in 46 appearances in all competitions.
The 33-year-old is seemingly keen for a new challenge at this stage of his career, and Barcelona are viewed as the favourites to sign him in the coming months.
However, Man United are said to be firmly in the race, and with that in mind, Sports Mole looks at how the team could line up next season, should the Red Devils manage to convince Bayern to let the experienced forward leave, in addition to signing leading target Frenkie de Jong from Barcelona.
Ajax's Jurrien Timber is believed to be admired by Man United, and it would certainly not be a surprise to see the Netherlands international arrive at Old Trafford this summer with a view to playing right-back next term.
Ten Hag has allegedly convinced De Jong to make the move to Man United, and the Netherlands international could play in a new-look midfield alongside Fred and Bruno Fernandes, with Scott McTominay and Donny van de Beek potentially being used as squad players.
Lewandowski's arrival could be a huge statement of intent, and it could mean a position change for Cristiano Ronaldo, with the Portugal international potentially moving out to the left.
Ronaldo has played the bulk of his career as a left-sided forward, and while he does not have the speed that he possessed in his younger days, the attacker certainly has the intelligence to operate in that area at this stage of his career.
Man United would have to find a way to play without cover down their left, with Fred and Shaw needing to play important roles defensively in that area of the field, but the 37-year-old could be even more effective for the Red Devils coming from a wide position.
Jadon Sancho could then move across to the right, forming an exciting front three with Ronaldo and Lewandowski, and not too many defences would relish coming up against the trio.
However, a lot would have to happen for Lewandowski to move to Old Trafford, and it could be a struggle to convince him to move to the club without the offer of Champions League football for next season.