United value Rose at around £45m and are hopeful of concluding a deal for the full-back before the World Cup.
It has been claimed that Rose is keen on a switch to United at the end of the season as he wants to work with manager Jose Mourinho.
"The lure of United is too strong for him and if he had the choice he would pick United hands down", said a source close to the Tottenham defender.
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Rose has not featured since suffering a serious knee injury back in zjanuary, but is set to return within a few weeks.
Rose was linked with a move away from Spurs in the summer, and aggravated the club through his conduct.
Spurs chairman Daniel Levy fined Rose and made him issue a public apology.
The Daily Star claim United are confident of landing the England global for £45million next summer and that the player has his heart set on the move going through ahead of the World Cup in June.
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Rose is contracted at the club until 2021 but is looking increasingly likely to leave.
Left-back has been something of an area of concern for Mourinho since his arrival at United with a number of players occupying the position so Rose would be the ideal long-term solution.
And a new left back ranks high on Mourinho's list of transfer priorities, with Daley Blind, Ashley Young and Matteo Darmian having shared the role so far this season.
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