The Poland international was thought to be close to a move to Old Trafford, with Sir Alex Ferguson believed to be a huge admirer of the 24-year-old.
But the Daily Star carries reports from Italian website TuttoMercato, which assert that Lewandowski is set to become Pep Guardiola's first signing at Bayern Munich at the end of the season.
The former-Barca boss takes over the German giants in the summer, and the report claims Lewandowski - who is out of contract at Borussia Dortmund in June 2014, could be tempted to the Allianz Arena for a fee in the region of £18m.
Defending Serie 'A' champions Juventus have also been linked with the striker, while United were reportedly weighing up a summer bid of their own.
But it seems both clubs have lost out, with the 2012 Champions League finalists ready to splash the cash once Guardiola takes the reigns.
The report claims the Spaniard could also move to bring in Liverpool forward Luis Suarez, as he looks to strengthen an already impressive-looking squad.
The German league leaders boasted one of the most formidable attacking trios in world football last season, with central striker Mario Gomez partnered by Franck Ribery and Arjen Robben.
But such is the strength-in-depth in Bavaria that Robben and Gomez have been overshadowed by another parntership this term, with Thomas Muller linking up superbly with summer signing Mario Mandzukic.