The report alleged that their relationship was suffering "serious strains" since the England captain's £25m move to Real Madrid this summer.
He had confided in a "close friend" that he was feeling lonely in Spain while she was in New York recording a new album, the newspaper said.
But the Beckhams, who have two young sons, insisted that they were very happy. The couple's statement said: "Contrary to newspaper reports our marriage is not in crisis.
"We are extremely happy together as a family. Our only difficulty has been finding a house in Madrid that meets our needs.
"Since we first met our careers have always meant we have spent time apart. This is not a reflection on the strength of our marriage and we are very much enjoying our new life in Spain."
The tabloid calculated that the singer had been in Spain for 33 days out of a possible 82. The 29-year-old has apparently been jetting between New York, Madrid and London.
The 28-year-old footballer's new life in Spain has attracted huge media interest including the appointment of "David Beckham" tabloid correspondents and an ITV documentary.
Beckham had been warned it would be a tough task to win over fans at the Bernabeu stadium but he enjoyed a dream start. The man once dubbed "Goldenballs" has also had success with his autobiography My Side.
But he has had less success finding a new home in Madrid, prompting him to make do with a five-star hotel life.
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