Ardian, a French investment firm, and Chinese conglomerate Fosun, withdrew their €17.5 per share bid after Andrea Bonomi made a higher offer at 21.0 per share.
Bonomi’s offer values the company at €790 million.
Ardian and Fosun announced on Thursday that they were pulling out, although people close to the matter said that Fosun might still have its eye on Club Mediterranee.
Ardian owns 8.3 percent of Club Med, and Fosun 10.0 percent, while Bonomi also owns 10.56 percent of the stock.
French stock brokers Gilbert Dupont said that the offer by Bonomi "now has every chance of succeeding."
The price of shares in Club Mediterranee was showing a fall of 1.07 percent to 21.22 euros in morning trading in Paris.
The Club Med board has been obliged reluctantly to consider the Bonomi offer.
The Ardian-Fosun bid, launched in May 2013, had won initial support from the Club Med board, with chief executive Henri Giscard d'Estaing arguing that it would leave the company under French majority control.
The matter became embroiled in litigation but the Club Med board ended up recommending that shareholders accept the Bonomi offer because it was substantially better, although directors said that the Italian bid raised concerns about strategy.
People close to the matter said that Gaillon Invest could not raise its terms because Ardian has a policy of not improving its bids.
But Fosun, a diversified group achieving strong growth from tourism might come forward with higher terms, particularly since Club Med wants to expand strongly in China.
A statement by Gaillon Invest said that Fosun was considering its options.
Bonomi, who has inherited a property and industrial fortune, wants to speed up Club Med's development in Asia, but also sees opportunities in France, Europe and the Americas.
Bonomi is interested also in expanding in the mid-range holiday sector, whereas Ardian and Fosun wanted to focus only on the top end of the market.