His company Bollore Group easily accounts for the largest shareholding in the media buying, market research and digital company, which was approached by WPP Group last November.
Bollore told a press conference at the end of March: "All options are open. We could strengthen our stake in Aegis."
Last year, the French corporate raider ruled out raising his stake in Aegis to more than 30%, the trigger point when he must make a full offer.
The comments by Bollore follow those of Sir Martin Sorrell, the WPP chief executive, earlier this year at the World Economic Forum in Davos, Switzerland, when he said he was still interested in buying media-buying rival Aegis and taking control of its market research business Synovate.
Sorrell abandoned a deal to buy Aegis with US private equity partner Hellman & Friedman in November. The plan would have seen WPP take control of the Aegis market research firm Synovate and take a small stake in the remaining media buying business while Bollore took control of media planning and buying operations Carat and Vizeum.
The media buying business could then have been linked with MPG, which is part of the Bollore-led Havas.
Under UK takeover panel rules, WPP must now wait until May before bidding again. A joint bid again with Bollore can not be ruled out.
In December, Bollore said: "We have the largest stake in Aegis. We have not invested for nothing, it's a financial stake. The game is open and we are open to reconsidering our position."
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