United boss Jose Mourinho hopes offering one left-back for another would smooth any negotiations with Tottenham chairman Daniel Levy.
Shaw could be on the way out of Old Trafford, according to the Daily Record (h/t Alex Porter of the Manchester Evening News), with the potential deal described as a "straight left-back swap."
Accepting Shaw in exchange for Rose seems rather fanciful. It is more likely the north London club would also demand some cash as part of the deal, especially since Shaw's career has stalled somewhat since he moved to United in 2014.
The 22-year-old found himself "criticised by Mourinho on a number of occasions last season and has one year remaining on the contract he signed when moving from Southampton in 2014," per Porter.
Shaw has had his share of fitness problems since arriving at Old Trafford and is recovering from a foot injury.
While Shaw has had his issues in Manchester, there is no doubt he is a talented full-back when healthy. Like Rose, the England international is a threat going forward thanks to pace and power in wide areas.
Shaw is also a competent defender, something Rose has matured into on manager Mauricio Pochettino's watch.
Despite any suitability regarding Shaw, Spurs are likely to still push for a lump sum should they opt to sell Rose during this transfer window. That's the view of The Sun's Dave Kidd, who noted how "Levy could now be willing to offload the Chelsea and Manchester United target—but not for less than the £50 million Manchester City paid for Kyle Walker."
Kidd also pointed out Premier League champions "Chelsea want Rose [...] and are more likely than United to make a bid before the window shuts on August 31."
It was during an interview with Kidd that Rose suggested he would accept a transfer elsewhere if he's not paid what he's worth, that sparked talk about his future. The defender later issued an apology for the timing of his comments through Base Soccer Agency:
Pochettino on Friday told the media the apology had been accepted, but Spurs may still be at the point of no return with their starting left-back. If so, the chance to salvage Shaw's undoubted potential may prove too tempting to pass up, especially if a fee is also involved.
Spurs are discussing a potential deal worth £35 million for the 21-year-old who can "play at centre-back or right-back," per Lewis. It is also noted how Sanchez was the Dutch club's player of the year last season and that his arrival would see Spurs break their transfer record.
Securing a highly regarded defender this versatile makes a lot of sense for Tottenham. Sanchez's ability to operate at right-back would help offset the loss of Kyle Walker, who joined Manchester City this summer, by easing the burden on Walker's replacement, Kieran Trippier.
In addition, Sanchez would also provide excellent cover for centre-backs Toby Alderweireld and Jan Vertonghen. He could be the heir apparent to the latter, who is 30.
Pochettino has built an excellent defence at Tottenham, one that was the stingiest in the Premier League last season, shipping just 26 goals.
However, Spurs need greater depth as they bid to battle on both domestically and in the UEFA Champions League.
Adding Sanchez—and possibly Shaw for Rose—would ensure things at the back remain rock-solid for Pochettino's squad.