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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Being an amiable guy is good for you and Jurgen Klopp is living proof.
Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.