Patrice Evra looks to be on his way out of Old Trafford eventually, and De Telegraaf, via Clive Burrows of The Independant, believe Alexander Buttner could be set for departure as early as this winter.
The Guardian's Jamie Jackson believes Shaw is David Moyes' fail-safe should he come up short in the Leighton Baines chase, with both players capable of locking up the left-back position for the next five years or more.
The Red Devils won't be alone in their pursuit of the Southampton starlet, though, as Chelsea's interest is both longstanding and, according to Paul Collins of The Daily Mail, fully endorsed by current incumbent Ashley Cole.
The only problem is pursuing Shaw this January is a fool's errand; a complete non-starter that won't end well for Cheslea or United.
Shaw is a boyhood Chelsea fan and was rejected the chance to join the club's academy when he was 12 years old. Given his current career trajectory, he will likely end up playing for them one day if given the chance. But this early in his career? Dream on.
The "bigger" Premier League clubs have a habit of ignoring the light and simply pursuing their targets with brute force, but stop to look at the circumstances and they'll realise they're better off waiting.
For a start, Shaw himself has stated—in Southampton's latest matchday programme—that he has no wish to leave at this moment in time, instead preferring to play first-team football for the next two years or more for the club who produced him, paid for him and supported him.
Of course, the lure of having £2-3 million put in your bank account is remarkably hard to resist for an 18-year-old, but Southampton's saving grace in this respect is their bulldozer of a chairman Nicola Cortese.
He is one of the most ruthless, cutthroat negotiators the Premier League has ever seen, but he's also got the money to improve Shaw's deal if the player starts getting restless.
Even if United and Chelsea convince Shaw and his agent this winter, they won't be able to overcome Cortese's brick wall-esque stance on the matter.
For England fans, Shaw staying at St. Mary's Stadium is the best possible outcome: He's a couple of years from assuming the first-choice left-back role for the national team, and to reach that goal he needs to play in a comfortable environment.
It's not fair to heap the pressure of a £30 million price tag on his shoulders this early, and unless you're a fan of the two clubs linked, it is nearly impossible to see sense in any deal taking place next month.
Shaw will be a Southampton player on February 1. Chelsea must be patient, and Manchester United must avoid yet another silly, ill-advised chase after an unobtainable player in what represents a critical month for recruitment.