Such a contract offer has allegedly seen the competition for the Southampton left-back's signature disappear, per Veysey's report:
Goal understands that Chelsea pulled out of the race to sign Shaw when they became aware of the £8 million-a-year, five-year contract offer that he had received from United.
Manager Jose Mourinho is a big admirer of the 18-year-old and is in the market for a left-back after releasing Ashley Cole but the Blues felt that they had been priced out of a move for the Saints youngster.
Veysey indicates that, while United's £27 million bid is yet to be accepted, "the fee is not blocking the sale."
Shaw has enjoyed a rapid rise to fame over the past two seasons and is currently preparing for the World Cup with England after an excellent season at St Mary's. The 18-year-old made an impressive 35 appearances throughout the 2013-14 Premier League campaign, where he showcased boundless energy and a natural affinity for supporting attacks from the left-back position, per WhoScored.com.
United have been linked with Shaw since 2013, when David Moyes failed in his attempt to lure Leighton Baines to Old Trafford, per Jamie Jackson of The Guardian. The youngster is certainly a long-term replacement to Patrice Evra and would offer the Red Devils a huge stride towards the future, unlike Baines, who would have represented a stopgap if he moved at the age of 29.
Shaw is said to have made his intentions perfectly clear, according to BBC Sport:
Evra's decision to sign a new one-year contract certainly adds to Shaw joining, per BBC Sport. The Frenchman will have top-quality competition for the first time in years—despite Alexander Buttner's best efforts—and is likely to help Shaw fit in before calling time on an illustrious career at the Theatre of Dreams.
It would make complete sense for Louis van Gaal to alternate between the two left-backs throughout a campaign in which United need to find their old impetus. Moyes' reign was marred by fruitless play, poor tactical decisions and a notorious inability to land transfer targets, a trend that may have indirectly impacted Shaw's future when Baines was missed out on.
Even so, Alex Harris of the Express reports "van Gaal has earmarked (Jordi) Alba as the ideal alternative with the player known for his ability to run from deep." Either the Barcelona star or Shaw would mark a huge signing for the club and crucial progress along the road to redemption after such a poor season.
Considering Southampton recently sold Rickie Lambert and are likely to sell Adam Lallana in the coming weeks, reported by Ben Smith of BBC Sport, the Saints will certainly be looking to receive top dollar for a youngster who ranks among the Premier League's best emerging talent.
Kevin Palmer of the Sunday World indicates Shaw's move is more likely to go ahead after Southampton announce their replacement for Mauricio Pochettino:
There's no doubt Van Gaal would be acquiring a player for the present and future if Shaw is secured. A suggested wage of £160,000 is certainly excessive, as one has to consider whether the player would agree to a deal with smaller terms. It wasn't long ago United were linked with offering him an £85,000-per-week contract, per Dean Jones of the Mirror; have the player's demands really doubled since March?
It is likely we'll find out across the next few weeks. Shaw will have a bit-part role at the World Cup but will be a useful replacement for Baines in the Brazilian heat and can certainly add to his reputation by playing fearlessly when he receives the chance.
United will hope to secure a deal before the Englishman can attract any further suitors, although it's difficult to suggest any club would match the aforementioned contract offer if it turns out to be true.