For more than four years, the activist hedge fund has been criticising the management and stock market performance of Lagardere, which has publishing, travel retail and media businesses.

Last month, Amber Capital, which has about 16.4% of Lagardere's shares, said it would propose its own list of new supervisory board members at Lagardere's annual shareholder meeting on May 5.

"They entered or are considering entering the capital of the publishing and distribution group in order to bring their votes during its May 5 General Meeting," Les Echos wrote, without citing its sources.

These stakes would be smaller than the regulatory threshold of 5%, so they do not have to be notified to French stock market authorities.

"It is a friendly gesture of support," one source close to the matter said, confirming the Les Echos report.

Bollore and Lacharriere could not be immediately reached for comment. Lagardere had no official comment.

Lagardere shares closed up 12.6% at 17.11 euros. They have rebounded 110% from an historic low of 8.14 euros set on March 17. The shares are still down 11.9% since the start of the year.

Amber Capital on Tuesday urged fellow investors to support proposals to replace the majority of Lagardere's supervisory board members, according to a letter shared with Reuters on Wednesday.

It received some backing of proxy advisor ISS, saying in a note "the appointment of five dissident nominees to a 12-member board appears warranted (...) given the apparent need for a robust dissident presence on the board".

Amber has criticised Lagardere's management and supervisory board for a "denial of reality" over the company's financial performance.

(Reporting by Gwenaelle Barzic, Marc Angrand, Dominique Vidalon. Editing by Jane Merriman)