"Tottenham insist there has not been a bust-up between player and manager," Mullock wrote, though he added that the Red Devils would be ready to double the left-back's £65,000 weekly wage if he were to make the switch to Old Trafford.
Mullock suggested United would also "offer his fellow England left-back Shaw in part-exchange" in order to expedite the transfer.
Rose was exceptional for much of 2016/17 until an injury curtailed his campaign early. Since then, he has struggled to force his way back into contention, with Ben Davies excelling in his place.
He has been involved in some fixtures lately, though when quizzed on his north London derby omission, manager Mauricio Pochettino said Rose wasn't fit enough to play.
"It's not strange," he said, per Rob Draper of the Mail on Sunday. "It would be strange for a player that is fit and playing regularly. But when you are 10 months and 11 months out and then you start to play, then sometimes the better decision is to be training and prepare for the next game."
Samuel Luckhurst of the Manchester Evening News remarked on Rose's position at Tottenham and how keen the full-back is to join United:
When he's at full fitness and in form, there aren't many left-backs in the Premier League capable of offering what Rose does. And while United are well-stocked in a lot of areas, the left side of the defence is where they have something of an issue.
Ashley Young has done well as a makeshift option, while Matteo Darmian and Daley Blind have also filled in at times. But Shaw has found it difficult to force his way into contention since Jose Mourinho took over as manager in 2016.
When the left-back arrived at the club from Southampton in 2014, he was expected to nail down the position for the long term at Old Trafford. Some bad luck with injuries and a seeming lack of trust from Mourinho have prevented him from making progress, though.
The United Stand Twitter account suggested a difference in personality hasn't helped Shaw settle under the Portuguese:
Pochettino has previously shown he's ready to make big decisions, such as pulling right-back Kyle Walker from the team last term. So if Rose does want to get back into the Tottenham starting XI, you sense he would have to put a lot of work in.
It would be a surprise if Tottenham were happy to sell a key player midway through the season, especially with the team involved in so many competitions. Still, Rose and Shaw's futures seem set to be topics for discussion throughout the campaign.