German publication Bild
It is no secret that United have shown a strong interest in the Germany international, with reports claiming the club have already had two bids turned down for his signature.
But fresh reports are now claiming that the 25-year-old has told the Bundesliga giants that he is keen to test himself at Old Trafford and would be interested in the opportunity to follow club legend Bastian Schweinsteiger to the club before the end of the current transfer window.
Muller kicked off the new Bundesliga season in superb style, bagging a brace as Bayern Munich trounced Hamburg 5-0 at the Allianz Arena on Friday night.
United are desperate to add more quality to their front line this summer, but it remains to be see has to whether Bayern will want to cash in on one of their most prized assets so close to the end of the transfer deadline.