The Duchess of York is "devastated" and "regretful" after newspaper claims she offered to sell access to ex-husband Prince Andrew, her spokeswoman says.
The News of the World said Sarah Ferguson was recorded by an undercover reporter posing as a businessman. She appears to accept $40,000 in cash.
The paper says the prince - a UK trade envoy - knew nothing about the alleged £500,000 ($723,000) deal.
The spokeswoman told the news agency PA the duchess regrets the incident.
According to the video soundtrack, the 50-year-old duchess tells the undercover reporter "£500,000 when you can, to me... open doors".
She also says the cash would "open up all the channels whatever you need, whatever you want, and then that's what and then you meet Andrew and that's fine.
"And that's, that's when you really open up whatever you want."
The newspaper says that the duchess told the undercover reporter, who was posing as an international business tycoon: "Look after me and he'll look after you... you'll get it back tenfold. I can open any door you want."
The News of the World says its reporter met the duchess twice - in New York earlier this month and in London last week.
In the first encounter in the US, the paper says she offered to arrange a meeting, allegedly saying: "What I want you to do next is to meet Andrew... as soon as you come to London, come to the Royal Lodge.
"I'll introduce you and sit down and you'll talk to him about whatever."
Then later in London, the paper quotes her again arranging a meeting with Prince Andrew. "I did ask Andrew about meeting you... I never talk about money ever, but since we've got business hats on I'm going to..."
It was then that she appeared to accept the $40,000 cash payment and go on to discuss the wire transfer of a further £500,000.
The duchess, who expected to pick up an award in the US later for her work with underprivileged children at a ceremony organised by children's charity Variety, is also quoted asking the reporter to donate 1% of profits on any resulting deals to her own charity.
But she also says her ex-husband, who has been the UK's Special Representative for International Trade and Investment since 2001, "never does accept a penny for anything" and describes him as "completely whiter than white".
In the newspaper, the duchess describes Prince Andrew as "so amazing".
"We're the happiest divorced couple in the world," she says.
But she also claims she is suffering financial hardship and that her divorce settlement entitles her to just £15,000 a year.
"I have not got a bean to my name. I'm a taxpayer, a British taxpayer and I left the royal family for freedom and in freedom it means I am bereft. I'm hopeless."
Earlier, the duchess's spokeswoman, Kate Waddington, said she had not been told about the meeting and was "incandescent" it had taken place.
She said the word "naive" sprung to mind.
The News of the World's royal editor, Robert Jobson, told the BBC the paper had pursued the story because it was in the public interest.
"What is very serious here is that she's so desperate that she's prepared to jeopardise the reputation of her ex-husband and of the country, and of an important international ambassadorial role, which is, after all, funded in terms of the expenses by the taxpayer," he said.
Sarah Ferguson married Prince Andrew in 1986 and the couple had two daughters, Beatrice in 1988 and Eugenie in 1990.
Although they separated in 1992 and divorced in 1996, she and their daughters later moved back into a wing of the former marital home and maintain a close relationship with the Duke of York.
The duchess's finances have been the subject of a number of negative headlines in recent years. In September, her spokeswoman confirmed court action had been taken over unpaid bills but denied the duchess had financial concerns.
BBC royal correspondent June Kelly said that after a period of cool between the duchess and the Royal Family, there had been a sense of "rapprochement" in recent times.
The newspaper claims would therefore be "very damaging" to that relationship, she added.
Buckingham Palace said it would not be making any comment.
Prince Andrew's role as UK trade envoy involves promoting British business at home and overseas.