CVC Capital Partners said it it has held talks with other investors, including existing Betfair shareholder and entrepreneur Richard Koch, about a possible joint approach for the online betting exchange.
Shares in Betfair surged as much as 17% on Monday, giving it a market value of about £790 million, but the company urged investors to do nothing and insisted its recently-revamped strategy will pay off.
The group was worth about £1.4 billion when it floated on the London Stock Exchange in 2010 priced at £13 a share, but has lost ground to competitors in recent years.
CVC said it has held preliminary discussions with Mr Koch, private equity investor Antony Ball and other partners about its options for Betfair.
Former management consultant Mr Koch has 6.5% of Betfair's shares and according to his website "made a fortune" from private equity investments including Filofax and Plymouth Gin. Mr Ball is a non-executive director of Luxembourg-listed investment firm Brait, which backed the buyout of frozen food chain Iceland in 2012.
Betfair's betting exchange works by matching punters and allowing them to bet against each other, which it says eliminates the need for a traditional bookmaker. It charges a commission on the bets. The company says it processes seven million transactions a day.
Betfair chairman Gerald Corbett said the company is going through one of the "most exciting phases in its development", thanks to a new strategy revealed in December, and has overhauled its management team, headed by chief executive Breon Corcoran.
Mr Corbett said: "Our management team is actively implementing the new business plan for the company and we remain fully committed to delivering on the new strategy and providing improved returns for our shareholders."