The French AMF market watchdog told the Italian interests, which have quietly built up a pile of shares in the resort group, to come out and say what they intend to do.
While waiting for the answer, the regulator blocked the bid, by Fosun and a French partner, from closing on Friday, extending the offer period by two weeks.
France's financial market regulator AMF ordered the Strategic Holdings fund of Italian financier Andrea Bonomi to restate what its plans were for its stake, after it recently disclosed it had become Club Med's biggest single investor with a 10.7-percent holding.
Club Med is a high-profile player in the French tourism sector but the global economic slump forced it to change strategy by moving upmarket.
The group broke the mould during the boom of package tourism in the 1960s and 1970s, offering trendy holidays in beach huts, using beads as money, and inspiring a series of French comedy films which have become classics.
But the group has escaped from that image, going more for the now older generation, investing heavily in international activities and aiming for substantial expansion in China.
In Asia, Club Med has been active in Japan for more than 20 years and also operates in Thailand, the Maldives and in Bali, Indonesia.
Fosun, which became a shareholder in 2010, began last year an effort to launch a takeover of Club Med, but small investors unhappy at the buyout price have frustrated its efforts
Fosun, together with the private equity fund of French insurer AXA, known as Ardian, were finally able to launch earlier this year a €550 million offer to take full controlof Club Med.
Small shareholders have been unhappy with the offer of €17.5 per share when the market price has been over €19, and there was even before Bonomi's incursion a serious possibility the takeover bid would fail.
Bonomi's investment vehicle said earlier this week when disclosing its 10 percent stake, that it had no intention of increasing its holding above the 30 percent level which would oblige it to make a public offer for Club Med.
It said this was it did not consider that taking control of the resort operator would be in line with its investment strategy.
However, the French business daily Les Echos reported on Thursday that Bonomi could in fact launch a share offer at a higher price than Fosun, as it estimates the fair value for Club Med shares to be between €21 and €25.
Fosun and Ardian failed on Friday in a legal bid to force the Italian Benetton firm to sell its 2.2 percent stake in Club Med after the Italian company, reportedly close to Bonomi, changed its mind last week.