Louis van Gaal is a long term admirer of Muller having been in charge of the Bavarian club when the 25-year-old first broke on to the scene.
German publication Bild had claimed the Red Devils had offered the fee for Muller, however Bayern's sporting director has moved to reject any claims Muller could be on his way to Manchester.
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As per the Guardian, Sommer said: “It is not Thomas who is causing the fuss, it is his performances. And we can’t do anything about that. [Chief executive] Karl-Heinz Rummenigge is right, he is a player that we cannot put a price on.”
Manchester United and Louis van Gaal are reportedly aware of the German club's stance on Muller, but are willing to push Bayern to the limit.
United have suffered a blow in their chase of Pedro, after it was revealed the Barcelona man will link up with Jose Mourinho and Chelsea.
Although Ed Woodward had reportedly flown to Spain to complete a deal, the Red Devils were not keen on paying £22m for the 28-year-old.
It appears Van Gaal's focus is now solely on bringing the World Cup winner to Old Trafford to link up with Bastian Schweinsteiger, however United are likely to face further disappointment.
The Red Devils have started the season with Wayne Rooney leading the line, however the England and Man United captain has failed to impress in the opening three games of the new campaign.
A deal for Muller, who scored 21 goals last season, would potentially see Rooney moved to the number ten role, but with a deal looking highly unlikely United fans will be hoping the 29-year-old rediscovers his form, and fast.