The club insist rumours of failed moves for the German pair are untrue, with a United spokesman saying: "It is not true that we made offers for Muller or Reus at any stage."
Bayern Munich striker Thomas Muller - one of the stars of his nation's victorious World Cup campaign with five goals - appeared to hint at an offer from United in an interview with German newspaper Sport Bild.
Asked if he knew of United's interest, Muller said: "Of course - I was aware I could theoretically earn more with a transfer.
"The sums that were standing by from foreign clubs were already astronomical. I can only say that a change was never really an issue anyway."
Meanwhile Atletico Madrid president Enrique Cerezo claimed in Spanish media that his club pulled out of the running for Reus because they could not match a more lucrative offer that United had already had rejected.