The England international, 27, has forged a reputation as one of the Premier League's best attack-minded full-backs over the past couple of years.
And his form for Spurs has seen him linked with a cluster of their title-chasing rivals, including United.
The Red Devils are thought to be interested in taking Rose to Old Trafford amid continued doubts about Luke Shaw's long-term future.
And the latest reports suggest Jose Mourinho wants the Leeds United academy graduate to bolster his backline.
According to Tutto Mercato Web, Rose remains a target for the United gaffer.
The transfer rumours specialists say Mourinho was after the defender over the summer.
However, Tottenham refused to do business.
The report also claims United could make a move for Rose in January.
They indicate Chelsea are keeping tabs on him too though.
Rose is currently out of action due to a long-term knee injury.
Tottenham, meanwhile, resume their Premier League campaign against Bournemouth on Saturday.
Mauricio Pochettino's men sit third ahead of the Wembley clash, five points adrift of early leaders Manchester City and second-place United.
It's unclear when Rose will return for Spurs.
When pressed for an update on the left-back last month, Pochettino said: "We cannot say in one week or two weeks.
"We are assessing them every day, still we need to wait and cannot give a date to return to the group and start training."
