Real are aware that contract talks between the 28-year-old striker and the Gunners have stalled, says the Sunday Mirror.
Van Persie will have just 12 months left on his current contract with the Gunners by the end of the season.
Real Madrid are considering making a move for Van Persie as Arsenal could be tempted to cash in on the striker, should they fail to get him to sign a new deal in the summer.
Manchester City are also reported to be keeping tabs on Van Persie.
