Tony Elliott, the chairman of rival travel publisher Time Out, told The Times yesterday that he had been told by "reliable sources" that the BBC was gearing up to sell the Lonely Planet business when it completes a strategy review next year.
, which was founded by Tony and Maureen Wheeler, who were left with a 25% stake valued at A$67.3m (£37m) before the credit crunch.
The Wheelers retained a put option when they sold the business to BBC Worldwide, which meant that they could force the BBC to buy their remaining shareholding at any time before October 31 this year, at which time the option would expire.
However, according to the Times report, BBC Worldwide has now voluntarily extended this put option to a new deadline because the Wheelers did not want to sell. The date of the new deadline was not revealed.
BBC Worldwide has strongly denied that it has plans to sell the Lonely Planet business.
A BBC spokeswoman said: "BBC Worldwide has no plans to sell the highly successful Lonely Planet travel information business. It is not up for sale full stop."
The Wheelers founded Lonely Planet in 1972 and the company now publishes hundreds of titles, including guides to visiting countries and cities on a budget, activity guides and phrasebooks. It publishes in an array of foreign languages, including French, German, Italian, Japanese, Korean, Mandarin and Spanish.
BBC Worldwide's acquisition of Lonely Planet was seen as a controversial move for the BBC because the purchase expanded the licence-fee-backed broadcaster into travel publishing — an area that had nothing to do with the BBC's core purposes.