WPP owns 22% of Tempus and could move to increase its stake in the company in an effort to thwart Havas. Havas's acquisition of CIA would give it extra clout in the media-buying world and would represent a challenge to WPP's position.
Sir Martin Sorrell is understood to have requested and received details on Tempus's financial standing.
Havas announced its move last week, when a £425m takeover deal was agreed with the support of Tempus chief executive Chris Ingram.
Some have poured cold water on talk of Sir Martin making a move for Tempus, as relations between him and Ingram are poor. The two have clashed at boardroom level several times.
In June, WPP was believed to be pursuing a share-swap deal that would see it swap its stake in media-buying group Tempus for a stake in larger rival Aegis, which owns Carat.
Such a deal would have seen WPP swap its stake in Tempus for a 5% stake in Aegis, which is valued at £1.3bn compared with minnow Tempus's £332m prior to the Havas bid.
Shares in Tempus remained high this morning at 552p, having reached 560p last week. Shares in Tempus soared more than 50% to 541p when the deal with Havas was first announced.
Last week, Alain de Pouzilhac, chairman and CEO of Havas, said he had not spoken to WPP about his bid for Tempus.
Sir Martin bought his shares in Tempus for 200p each and might simply launch a counter bid in an effort to force Havas to pay more. This will increase the value of Sir Martin's stake and the profit WPP makes on the deal.