The Argentinean showed that he was not on top form in the Champions League clash with the Reds last week and it's said that there is interest being sniffed out by the player's agent as well as representatives of Real.
It is also thought that Real will be in for snapping up Gareth Bale from Tottenham in the summer and if this is the case, they need to make way for the new boy.
The Reds have already revamped their wing options for next season by signing Wilfried Zaha from Crystal Palace and the England international went off in his side's 2-1 win over Bristol City last night with a "minor impact injury", according to Eagles boss Ian Holloway.