Bollore, who has a reputation as a corporate raider and had voiced his disapproval for Havas' takeover bid for Grey, now has five days to publicly state his intentions for the group.
He first began buying up shares in the summer, taking a 4%-5% stake in Havas in July, just after the company had said it was interested in taking over Grey Global Group.
After Havas lost out to the WPP Group in the battle for Grey this week, a spokesperson for Bollore said that they were "satisfied" with the result.
Shares in the company were trading heavily today, with 2.53m changing hands. This afternoon, the price was €4.25, a rise of 2.41% on the opening price this morning.
Havas is due to publish its interim results tomorrow and there have been reports that chairman and chief executive Alain de Pouzilhac will face calls from shareholders to step down from his role.
Rival French group Publicis Groupe and WPP are tipped as the most likely buyers if Havas does go up for sale.
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