Marca claimed that during a short telephone conversation with the player on Thursday the Netherlands international had been buoyed by reports that Los Blancos were keen on signing him.
"I am pleased to hear about the interest from such an important club as Real Madrid," Van Persie allegedly told the Spanish daily.
"Of course I would like to play there ... [But] I don't think Arsenal will agree to negotiate."
However, the player himself has moved to dismiss the veracity of the article on his Twitter profile.
"Contrary to reports in Spain I have NEVER spoken to Marca newspaper and never gave any interview. Enjoy your day," the in-form striker wrote.
Van Persie, who has struck a career-best total of 28 goals for the Gunners already this season, has been linked with both Madrid and Barcelona in the last few weeks.
Madrid coach Jose Mourinho was in the market for a top striker last summer, but was frustrated in his attempts to bring in Sergio Aguero from Atletico, with the Argentine eventually signing for Manchester City in a deal worth around €40 million.
And despite the positive form of both Karim Benzema and Gonzalo Higuain this season, Mourinho is still thought to be keen on signing a world-class frontman.
How do you stay up to date with football when on the move? With http://m.goal.com – your best source for mobile coverage of the beautiful game.