According to Sport1 (via The Mirror), United have made contact with Bayern over a possible transfer of the German centre-back.
Ole Gunnar Solskjaer is believed to have made it clear to Ed Woodward that he doesn't want a repeat of last summer, where United failed to sign a defender.
United have been linked to a host of Europe's top centre-backs, and Süle is the latest to have been approached.
Bayern signed Süle for £21m from Hoffenheim two years ago, but the 23-year-old has three years remaining on his deal, meaning it will take a substantial bid to prise him away.
A starting offer of about £40m is reported to be a sensible starting point.
Kalidou Koulibaly, who has been linked to United this summer, is still unsure about his future, while Mathjiis de Ligt of Ajax is reportedly close to agreeing a move to Barcelona.
With the market shrinking somewhat, United are keen to make progress in their hunt for defenders.
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