Jose Mourinho has made it his priority to sign a left-back, with doubts persisting over Luke Shaw.
The Portuguese tactician questioned the player’s commitment earlier in the season and claimed he was a ‘long way’ behind his team-mates.
Rose has found himself linked to United and City, and could earn a lot more were he to leave Spurs for either one of them.
And according to the Daily Mirror, United are leading the race for his signature.
Mauricio Pochettino is looking at potential replacements were Tottenham to lose Rose.
Manchester United summer transfer targets Wed, May 24, 2017
Express Sport takes a look at who could be on Manchester United's shopping list this summer
Play slideshow Getty Images 1 of 10
Manchester United are exploring a deal for Danny Rose
Tottenham could swoop for Luke Shaw if Danny Rose leaves
There is only so much the club can do. A lot of it has got to be down to the individual
Get Quotes on Home Insurance
It is said Daniel Levy will fight to keep hold of the club’s players and are desperate to ensure there aren’t a spate of exits.
Rose admitted last week Spurs can’t stop their best players from leaving, as he said: “There is only so much the club can do. A lot of it has got to be down to the individual.
"Someone like Harry Kane, I can tell you that his mindset will be 'I'm staying at Tottenham, I'm going to break every single record, I'm going to captain this club into the new stadium' so when you've got a player like him with that mindset I don't think Tottenham have to worry.
"But it depends where the individual is in the stage of his career.
“He might feel he has done enough at Tottenham and might fancy a change or might feel Tottenham is the nearly club that nearly wins the league and might choose to move on."
Should Tottenham sell Rose, it could prompt them to make a move for Shaw.