It has not been ruled out at Liverpool that the Argentine could be sold this summer.
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It is said to be likely that management will need to make a decision to either extend the midfielder's contract or sell him.
Real Madrid are seeking a new midfielder for the summer market.
The Athletic reported yesterday that former coach Carlo Ancelotti requested Mac Allister during his time with Real Madrid.
Real Madrid have also received positive feedback previously from Mac Allister's camp when in contact.