(Adds further details, background, share price)
PARIS May 26 Funds led by Italian businessman Andrea Bonomi could make a counterbid for Club Mediterranee , saying on Monday they would first need access to the French holiday group's books before making a decision.
French markets regulator AMF had asked for clarity on the funds' intentions towards Club Med after one of them, Strategic Holdings, became Club Med's top shareholder with a stake of more than 10 percent earlier this month.
Club Med shareholders had been due to finally decide on whether to accept a long-delayed 557 million-euro ($760 million) offer by Chinese conglomerate Fosun, French private equity firm Ardian and management by Friday, but the AMF extended the deadline to June 6.
Bonomi's Investindustrial Development said AMF rules had forced it to "engage the means necessary for the launching of a possible tender offer for Club Mediterranee, in order to avoid the risk of being blocked from considering a possible offer at a later stage".
Strategic Holdings said in a separate statement that it could consider teaming up as a minority shareholder in a private investment company led by Investindustrial to make a tender offer for Club Med.
Investindustrial said it would need five weeks to decide on a possible offer once it had full access to information on Club Med, adding that it would only make a bid with the support of the company's board of directors.
Fosun-Ardian's year-old offer of 17.50 euros a share through bid vehicle Gaillon Invest had delayed by litigation and sits well below Club Med's current 19.16 euros share price.
Investindustrial said it expected Club Med directors to back a rival offer that was at a higher price than the current bid.
Founded in 1950, Club Med was a pioneer of the all-inclusive holiday resort. But it has faced tough competition in the last decade in which it made an unsuccessful expansion into services. Club Med's more recent drive to recast itself as an upmarket operator has also been hampered by a weak European economy. ($1 = 0.7325 euros) (Reporting by Dominique Vidalon; Editing by James Regan and Greg Mahlich)