The Guardian reports that Moyes is a long-time admirer of the Croatian midfielder.
Real Madrid are reportedly prepared to sell the 27-year-old if United make a bid in the region of £25million for the midfielder.
Modric joined Real Madrid from Tottenham for £33million last summer, but failed to impress under Jose Mourinho at the Bernabeu.
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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?