Fosun, which has brought Brazilian investor Nelson Tanure on board as a minority partner, is upping its bid 50 cents a share to €23.50 - over the latest €23.00-per share offer made by Italian businessman Andrea Bonomi.
Fosun and Bonomi are locked in a bidding war for club Med, whose board in early October approved the earlier Fosun offer as "more with the interests of the company".
The improved Fosun offer was being lodged Monday with French stock market regulators, just hours ahead of a deadline for that to be done.
Speculation that the offer could go higher still drove Club Med's price up to €24 per share in late morning trading Monday in Paris.
Club Med first became a high-profile name in the European tourism industry for its all-inclusive budget family villages.
It has since moved up-market, weathering financial storms in the process, and is now looking for further expansion, including in China where it has been a partner with Fosun.