The Daily Mail is reporting that Jose Mourinho has identified the Gunners’ top scorer as the ideal summer sigining.
Van Persie’s deal at Emirates Stadium finishes in 2013 and if Arsene Wenger cannot convince him to sign a new contract, he could be forced to sell the striker.
The Holland international has been in scintillating form over the past year, scoring 35 goals in 2011 and already reaching 28 in 31 games this season.
The report also suggests that Real’s La Liga rivals Barcelona have made the 28-year-old their number one summer transfer target.
Wenger will be desperate to convince Van Persie to pen an extension to his current deal and avoid a situation similar to that of Samir Nasri last summer, where the club was forced to sell him to rivals Manchester City.