There's been claims Alexander-Arnold has been informed by Real chiefs that he should find himself another club in the summer - claims that have since been denied by coach Alvaro Arbeloa.
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Asked about the prospect, Murphy told BestBettingSites: “No. I think that would be a difficult one to sell to the fans.
“Also, not many players go back to a former club and succeed.
"The succession plan has to be about moving forward and evolving the team. So no, I don’t think that would work.”
Alexander-Arnold has made just 11 appearances in all competitions for Real this season.