The report in Le Monde newspaper emerged with Hollande on the defensive after his former budget minister, Jerome Cahuzac, was charged in a tax fraud probe after he admitted to having a secret foreign bank account and repeatedly lying about it.
Based on an investigation using leaked records, Le Monde reported that Jean-Jacques Augier, a 59-year-old businessman and the treasurer for Hollande's presidential campaign last year, had shares in two companies registered in the Caymans, a well-known tax haven.
Asked by the newspaper, Augier confirmed the existence of the firms and said they had been set up to form partnerships with foreign entrepreneurs.
"There is nothing illegal," Augier told Le Monde, which carried out the probe with the Washington-based International Consortium of Investigative Journalists and other international media.
The first firm, International Bookstores, was set up in 2005 so Augier could form a partnership with a Chinese businessman, Xi Shu, to break into the country's retail bookselling market, Le Monde said.
Augier said his partner had insisted on registering the company in the Caymans.
A second firm was created in the Caymans three years later, this time with a group of international tour operators, Le Monde reported. The firm has since been moved to Hong Kong, it said.
Augier denied any wrongdoing, saying: "My adventurous nature is responsible. Maybe I lacked a bit of caution."