Jan-Christian Dreeson, the Bundesliga club's financial partner, has told Bild that the Red Devils offered £85m for the Germany international.
"There really was such a thing," he said. "Then came a fax from England. For us, however, a sale of Thomas Muller was never discussed.
"If a player fits us, we would be stupid to give him a short-term prospect of a record profit and to weaken him."
Meanwhile, the Red Devils have been linked with a big-money move for Atletico Madrid forward Antoine Griezmann at the end of the season.