The German press reports that GfK chief executive Klaus Wuebbenhorst said: "We have until September to present a friendly offer. We will use this time."
The same reports suggest that GfK may well look at other, unnamed, acquisition targets.
GfK has variously been reported to have held talks with private equity groups Apax Partners, Cinven, and a German billionaire, Gunter Herz, over funding but is yet to make an offer.
This has angered WPP chief executive Sorrell, who has already made a £1.08bn hostile offer for TNS. Last week he told journalists: "They are misleading the market. They say they have access to an unidentified but substantial source of capital. It is time to put up or shut up."
The TNS board has urged shareholders to reject WPP's offer, and is angling for a deal with GfK.
Market research firms may not often get the international media worked up, but the battle over TNS has turned out to be one of the brighter points in a summer dominated by City stories of fears over the state of the economy and profit warnings.
TNS chairman Donald Brydon has accused Sorrell of trying to "screw us up", and Sorrell hit back saying he must be living in "dreamsville" if he thinks that is WPP's motivation. There have also been arguments over whether or not WPP has had access to all the financial data that has been made available to GfK.