But the Reds are in for a shock, according to Spanish publication Marca, who claim a surprise return to his former club is on the cards for Illarramendi.
The 25-year-old left his boyhood club for the Bernabeu in a deal worth around £23m in 2013.
He has since made 59 La Liga appearances but appears to be out of favour with new manager Rafa Benitez.
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Asier Illarramendi is reported to be on his way to former club Real Sociedad
And Sociedad boss Moyes could be ready to set up an emotional reunion, while doing his old club United a favour at the same time.
Moyes was a resounding flop at Old Trafford but might well have a dealt a blow to one of their Premier league rivals by concluding a deal.
The Scot is reportedly willing to match Reds boss Brendan Rodgers' offer of £15m and Illarramendi is understood to prefer a move to another Spanish club.
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