The report was based on seemingly contradictory comments about the 31-year-old midfielder made by Real president Ramon Calderon, speaking in English, to BBC Radio.
Real and Beckham's representatives are discussing a two-year extension to his current contract, which expires in 2007, that would keep him at the Bernabeu until 2009.
"We are trying to sign a new contract," Calderon told BBC Radio Five Live. "I hope we can have him forever -- but I'd say it (the contract) is going to be two years."
Calderon then muddied the waters by saying: "As far as I know, he has decided to retire in two years' time. It would be fantastic if he would stay with us for the next two years."
However, Beckham's spokesman told Reuters: "Talk of retirement is a complete surprise to us. No one has ever discussed a retirement date.
"David's only concern is to play for Real Madrid and win things at the club."
Asked about Calderon's comments, spokesmen for Real Madrid and Beckham both said the aim was for the former England captain to stay for two further seasons after the current campaign.
Pressed about Beckham's retirement plans, Calderon indicated his view was not based on anything the player had said to him but from "what people said to me."
Beckham, who has a football academy in Los Angeles, has more than once expressed an interest in ending his career in the United States.
He told the Web site of US broadcaster ESPN in April: "Playing in America is possible. I've one year left at Real, and maybe two more after that, but things can change in football and the American league does interest me."
AMERICAN SWANSONG
Calderon seemed well aware of a possible Beckham swansong in the United States.
"I read somewhere that perhaps he's going to the States for a golden retirement," he said.
"I'm quite sure that nowadays a player at 34 or 35 can play easily. Especially him, who's a great professional, he's been training all his life.
"He does things in the right way. I imagine that if he wants, when he leaves Real Madrid, he can be anywhere in the world -- in the States perhaps, why not back in England?"
As for Beckham's immediate future, Calderon said: "We need him.
"He's playing very well. The coach trusts him. We hope everything will be arrived at in the next 15 to 20 days to sign the new contract."
Despite the praise, Beckham has lost his place in the starting lineup under new coach Fabio Capello with the arrival of loan signing Jose Antonio Reyes from Arsenal and has started the last four games on the bench.
Beckham, still one of the most famous faces in sport, has not won a major trophy with the Spanish club since joining in 2003 from Manchester United.
He relinquished the England captaincy after their World Cup exit and has not made the squad since. New coach Steve McClaren has moved Steven Gerrard into his role on the right flank and made Chelsea defender John Terry his new captain.
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