"I have seen stories in the media linking me with Real Madrid," the 21-year-old Spanish international striker told Premier League champions Arsenal's official website.
"Of course it's flattering but not only am I under contract at Arsenal, I am happy here and committed to helping the team win more trophies."
An impersonator from the radio station rang Reyes pretending to be Real Madrid's sporting director Emilio Butragueno.
Unaware he was not talking to the real Butragueno, Reyes told the impersonator in a live show that he was keen on a move to Real.
"I am delighted that Real Madrid are interested in me because I have always wanted to play there," Reyes told the radio station.
"God willing, it can happen. The way things are (in London) at the moment, I'm not happy."
Arsenal paid a club record fee of around 17 million pounds ($31.62 million) to Sevilla for Reyes in January 2004.
