The Red Devils have been linked with a move for the Poland international in recent days following the departure of Robin van Persie to Fenerbahce.
Lewandsowski had a mixed first season at Bayern Munich following his controversial move from Borussia Dortmund last summer.
Former Liverpool midfielder Thompson is fearing the prospect of the 26-year-old linking up with Louis van Gaal’s new-look United side.
— David Thompson (@77thomo) July 20, 2015
The Pole scored 17 goals in 31 Bundesliga appearances for Bayern last season.
Lewandowski helped Pep Guardiola’s side win the Bundesliga crown in his first season at Allianz Arena.
Van Gaal, who was appointed as David Moyes’s successor last summer, has already signed four players in the summer transfer window.
The Red Devils snapped up Netherlands international Memphis Depay, Southampton midfielder Morgan Schneiderlin, Italy and Torini full-back Matteo Darmian and Bayern Munich midfielder Bastian Schweinsteiger.
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