Asier Illarramendi
The deep-lying midfielder fell out of favour under Carlo Ancelotti at Real Madrid, making only 10 league starts last season.
It remains to be seen whether Rafael Benitez sees a future for the former Spain U21 international at the Bernabeu, and van Gaal has previously been reported to hold an interest in the former Real Sociedad man [Daily Star].
He could prove to be an ideal long-term replacement to both Michael Carrick and Schweinsteiger.