Spanish media reported on Tuesday that Real had set their sights on the player and would seek to bring him to the club in the winter transfer window. Less than a week ago, Arshavin, 27, told Russia's Sport Express newspaper that he would not play for his hometown club next year.
However, the Spanish Sport daily said that Real trainer Bernd Schuster was not interested in Arshavin, and that he was seeking a replacement for injured forward Ruud van Nistelrooy. The paper said that because Arshavin and the Dutch international are entirely different types of players, the Russian did not feature in his plans.
The paper also reminded its readers that Arshavin was cup-tied for this season's Champions League, having already played for Zenit in the tournament.
"At the moment these are only rumors," Arshavin told the Russian Sport Express paper when asked earlier about possible interest from Real. "There is no point in commenting on them. One thing should be understood though - the most important thing here is not any interest in me by Real or anyone else, but if Zenit will want to let me go."
Arshavin became a target for a number of European sides this summer after helping Zenit lift the UEFA Cup and then propelling Russia to the semifinals of Euro 2008.
Although the diminutive forward made no secret of his desire to "test himself abroad," Zenit, controlled by state-run energy giant Gazprom, subsequently turned down offers of some $20 million and $26 million from Barcelona and Tottenham Hotspur, respectively.
Top Zenit club official Konstantin Sarsaniya said on Tuesday, however, that the club's $32 million asking price would probably be lowered.
"There are objective reasons for this - firstly, the player has not got any younger, secondly the global financial crisis has had an influence on the price," he said.
English Premier League club Tottenham Hotspur are rumored to be considering a new bid for Arshavin when the transfer window opens on January 1.