Havas has already extended its offer once and that deadline for Tempus to respond expired today.
Havas had been expected to come back with a higher offer, but so far it has resisted.
Last week, WPP issued its formal offer document for CIA-owning Tempus. The WPP document gave Tempus shareholders until October 1 to accept WPP's offer.
Havas's original July 541p-a-share bid for Tempus valued the company at £425m. WPP CEO Sir Martin Sorrell trumped this with a 555p-a-share counter-bid, valuing Tempus at £437m.
Alain de Pouzilhac, the Havas CEO, has been biding his time since the WPP bid. Analysts have been expecting Havas to come back with a bid which could be as high as 575p a share.
If this happens, analysts believe that it is unlikely WPP will counter-bid, but will instead take the money and prepare for a possible bid for Tempus's larger rival Aegis, which owns the Carat media-buying group.
WPP already owns approximately 22% of Tempus, bought earlier this year at an average price of 220p a share.
It would like the Tempus directors to walk away with millions in profit. In WPP's case, this cash could form part of a war chest to buy Aegis, which is valued at around £1bn.
Havas, if successful, plans to combine CIA with its own media-planning and buying unit, the Media Planning Group.
In WPP's case, it has said it would combine CIA with its second-string media network, The Media Edge.
In both cases, the mergers would create the world's fourth-largest media-planning and buying network.