"We don't comment on rumours or speculation but I can say that the story in the (Daily) Mail isn't true," a club representative told Reuters on Friday without elaborating.
Smalling has not played since the 4-0 defeat at Chelsea last month.
Manager Jose Mourinho appeared to question the commitment of Smalling and left back Luke Shaw after the two England internationals missed Sunday's 3-1 win over Swansea City.
The Portuguese said Smalling "doesn't feel he can play 100 percent without pain", adding there was "a difference between the brave, who want to be there at any cost, and the ones for whom a little pain can make a difference".
Both players were overlooked for England's World Cup qualifier against Scotland at Wembley on Friday with interim manager Gareth Southgate telling reporters "they are not fit and that's ruled them out for us this time".
He did not specify what the injuries were.
"Obviously it's a difficult one because I don't know the reason for the comments Jose's made," said Southgate.
United, who are sixth in the Premier League and trail leaders Liverpool by eight points after 11 matches, play their next fixture at home to fourth-placed Arsenal on Nov. 19.
(Reporting by Steve Tongue; Editing by John O'Brien and Tony Jimenez)
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