AXA Private Equity and China's Fosun are behind the bid, which Club Med's management described as "friendly".
Club Med shares jumped 23% on Monday in response to the offer.
Club Med pioneered the all-inclusive holiday resort in the 1950s and 1960s, but has recently struggled amid the economic downturn in Europe.
Analysts suggest the bid will see the company accelerate its shift towards faster-growing markets, particularly in Asia, as well as continuing efforts to move more up-market.
Club Med operates about 70 resorts worldwide.
In a statement, its management board said it "took note of the friendly character of this offer" and would meet again to give its opinion, following a report on the bid by independent analysts.
AXA Private Equity and Fosun are two of Club Med's biggest shareholders. They said that the current management, including chairman and chief executive Henri Giscard d'Estaing, would remain in place if the bid was successful.
French holiday firm Club Med looks set to be taken over by two of its shareholders in a deal that values the company at 541m euros (£463m; $700m).