However, the Mirror have reported that Everton are now hot on the heels of United in pursuit of the left-back's signature. It is understood that Sam Allardyce is looking for a successor to long-serving local lad Leighton Baines.
Baines, who will turn 34 in December, has been at Everton for 11 years. The Blues see Rose, 28, as his long-term replacement.
Manchester United's season-long interest in Rose has cooled of late, with the club concerned over the Englishman's injuries this season, which has seen him play just 16 games.
It is reported that the Spurs man earns £60,000 per week, but Rose could most likely double his salary were he move to Old Trafford rather than Goodison Park.
However, Everton are believed to be ready push through the move, but Spurs are certain to play hard ball over a fee in the region of £37m.
Swansea centre-back Alfie Mawson is also on the radar at Goodison Park, but the Toffees face strong competition from West Ham and Leicester for his signature.
With Swansea likely for the drop, Mawson could be wearing blue on Merseyside very soon.