The Daily Star reports that United boss David Moyes is considering making a January bid for the Southampton defender.
But Shaw could decide to turn down the chance to join United as he dreams of joining Chelsea.
A Saints insider told the Daily Star: “Luke’s a huge Chelsea fan and he’d be delighted to play for them.
“United’s interest is flattering but he knows he doesn’t have to rush anywhere just yet.”
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The start of the 2017-18 Premier League season is just around the corner and is shaping up to be one of the most competitive yet.
As always it is the so called “big clubs” that have splashed the most cash in the transfer window so far this summer. Manchester United or City? Arsenal or Tottenham? Who are the winners and losers of the transfer window so far?