The Red Devils are seeking a January deal for the left-back, who would be 'interested in a move away', according to 'The Sun'.
Rose has controversially voiced his displeasure at Spurs' transfer policy and claimed he was 'worth more' than he was getting.
Despite the 27-year-old hinting at a move elsewhere, chairman Daniel Levy is determined not to sell to a Premier League rival.
A source said: 'It is not secret that Jose likes Rose. He is looking to make a move for him in January when the window opens.
'He could prove difficult to get though as Tottenham do not like dealing with United. It all depends on money at the end of the day.'