However, if United feel as though they need to beat the competition, and Rose feels like his chances of starting for England at the World Cup depend on it, then there remains a slight chance he'll be heading north in a month's time.
Jose Mourinho will prioritise full-backs for Manchester United in the January transfer window, and is considering acting on the club's long-standing interest in Danny Rose of Tottenham Hotspur. The Red Devils were interested in him last summer but the north London club refused to sell, having already sold Kyle Walker in the same period.
Shaw has been linked with a move to Tottenham Hotspur over the past few months with Pochettino now in charge at the north London club.
Spurs Name Rose Price - United Poised
Should Rose move to Old Trafford, it is likely he would double the £80,000-a-week he is now earning at Spurs.
The report suggests that Tottenham boss Pochettino is now willing to cut loose his pacey left-back, and has instructed his talent spotters to unearth another option of similar ilk in order to help Spurs' defensive cause.
Mourinho is also conscious of his former Real Madrid player Mesut Ozil's contract situation at Arsenal, with his deal set to run out of the end of the season, but it is expected United would try to get him then rather than prise him away from the Emirates for a fee in January.
United admit that agreeing a deal with Spurs chairman Daniel Levy - a very tough negotiator - will be an arduous task.