In morning trading, WPP shares fell 4.2% to 704p having closed last night at 736p.
Tempus is currently the subject of a friendly takeover bid by French group Havas Advertising. Havas made a £425m bid for Havas or 541p per share.
The city has been waiting for the last three weeks to see what Sir Martin Sorrell, the WPP CEO, would do. WPP owns 22% of Tempus and has been studying the company's financial records for the last two weeks.
WPP paid only 200p for its shares in Tempus and, according to reports, it could afford to spend up to 650p per share on a bid for Tempus.
For WPP, the buy would be a good one. CIA, the Tempus-owned media-buying network, is strong in Europe while WPP's Media Edge, acquired when WPP bought Young & Rubicam last year, is strong in the US.
A merger of the two would create a powerful media network, which could sit well alongside WPP's other media-buying network MindShare, which is more evenly balanced between Europe and the US.