One of the club's directors told Spain's biggest-selling football magazine Don Balón that while publicly Real have said they want him to stay for two more years, they would prefer Beckham to quit.
The unnamed director, a member of the club's 18-man board, is quoted as saying: "We can't admit it but it would be best for both sides if Beckham left.
"[Coach Fabio] Capello doesn't want him and [Beckham] can't carry on as things are, spending so much time on the bench because it would lose him some of his multi-million-pound advertising deals. It's no good for the club either, to have such a famous player on the sidelines like a ticking time-bomb."
The claims, which will increase speculation that Real Madrid could even try to sell Beckham in January when he would still command a fee, also suggest that Capello does not want to keep Beckham. The article quotes a member of Madrid's technical staff saying: "Why would we invest £16m over two years on a player who is not to the liking of the coach?"
The Beckham camp last night dismissed the interview. A spokesman said: "We are dubious about comments made by an unnamed member of the board. If it is true, it goes against everything Capello, Ramon Calderon and Pedrag Mijatovic have been saying to us and to the world's media, that they want him to stay. Talks are ongoing and positive and we expect another meeting very soon." Real president Calderon, sporting director Mijatovic and Capello have all said they want Beckham to stay.
But the unnamed director added: "What Calderon said two months ago is one thing and what he wants now is another thing entirely. Capello prefers a different type of player and, in the club, everybody would be relieved if Beckham, of his own accord, said he was going to play in the US. That way, nobody could throw it back in Calderon's face that he was the one who had dispensed with the services of an icon like Beckham."
Beckham has started just three league games and one Champions' League match under Capello and has admitted he could not stand a further two years on the bench. And with MSL clubs now allowed to break their wage cap for one player, a move to the US looks an increasingly viable option and there will be no shortage of clubs in January tempted by the prospect of talking to Beckham, who will be free to begin negotiating a move away from Spain.
While two Real veterans, Roberto Carlos and Guti, have both agreed new deals this week, Beckham's talks remain ongoing and club figures such as former manager and Champions' League winner Vicente Del Bosque have expressed their doubts over giving him a new deal.
Del Bosque said: "He has had a brilliant career and his conduct is always excellent. The economic marriage between Beckham and the club could be important but if he is not in the team it is bad business."
Spanish magazine Don Balón was last night standing by its boardroom revelations. Real, who have been known to use the press to leak stories, were given the chance to comment but declined to do so.