According to The Sun, Jose Mourinho wants to sign the north London club's left-back when the transfer window re-opens in January.
Rose has not played in the Premier League since the start of 2017 due to a knee injury but is back in training and close to a first-team return.
Prior to his injury troubles, the 27-year-old had been in outstanding form prior to his injury setback and had established himself England's first choice-back.
Rose angered Spurs chiefs back in August when he gave an explosive interview criticisting the club's lack of transfer activity and admitting he would be open to leaving.