The Germany defender has long been a target for several top European clubs and he recently said he would like to play abroad at some point in his career. Hummels' current deal runs out in 2017.
German media have been full of reports in recent days of a possible move at the end of the season and an alleged promise he had made to the United coach that should he decide to move that he would join the English club.
But the central defender, who won the World Cup with Germany last year, said this was false.
"Just to be clear. This alleged "promise" is simply an invention... and that is saying it nicely," he said on his official Twitter account on Wednesday.
Dortmund, German champions in 2011 and 2012, have been struggling this season after a bad first half and are in 10th place, chasing a European spot with eight games left in the campaign.
Dortmund take on Bayern Munich in the Bundesliga on Saturday.
(Reporting by Karolos Grohmann; editing by Sudipto Ganguly)
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