The England defender has put clubs on high alert after an explosive interview this week which saw him question the ambition of the Spurs board.
The 27-year-old also expressed his desire to one day return to playing in the north of England - which inevitably saw United's name come into the frame.
Old Trafford sources, however, say that whilst Rose is a player they have previously kept tabs on, the club is not contemplating a bid for his services.
United boss Jose Mourinho is a fan but his priority remains on trying to sign winger Ivan Perisic from Inter Milan during the remainder of the window.
Spurs would demand in excess of £50m for Rose and Mourinho has already told Luke Shaw and Matteo Darmian that he expects them to be fighting it out for the left-back slot this season.