Argentinian defender Rojo arrived in Manchester by private jet on Wednesday to discuss personal terms and undergo a medical after United agreed a £16million fee with Sporting Lisbon.
But United insist rumours of failed moves for the German pair are untrue, with a United spokesman telling Press Association Sport: "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.
Despite the near-certain completion of a deal with Rojo, United appeared to suffer more frustration in the transfer market on Wednesday when Marouane Fellaini reportedly sustained an injury in training.
United have not commented on the extent of the injury, but pictures in The Sun showed the 26-year-old on crutches with his left foot in a protective cast.
Fellaini had been expected to tie up a loan move to Serie A club Napoli before the end of the transfer window and that move is clearly now in doubt.
New United boss Louis Van Gaal has made it clear he does not see a future for Fellaini at Old Trafford despite mounting injury problems at the club.
Fellaini's midfield partner Michael Carrick is already ruled out for around two months with an ankle injury, leaving Ander Herrera, Tom Cleverley and Darren Fletcher as United's only fit central midfielders.
Fellaini has endured a disappointing career at Old Trafford since his £27.5million move from Everton on transfer deadline day last summer.
He was booed by some United fans during the pre-season win over Valencia but also scored the winning goal.
Fellaini appeared as a substitute in Saturday's Barclays Premier League defeat to Swansea, replacing Herrera for the last 23 minutes of the match.
Source : PA
Source: PA