Apax has held early discussions with GfK in the past week, however there is no certainty that the two companies will reach an agreement, according to a report in The Times.
GfK, which is also still believed to be in talks with Gunter Herz, the German billionaire, and his sister Daniela Herz, said last week that discussions to raise funds for a rival bid were "progressing positively".
The German firm must find the necessary cash to beat WPP's £1.08bn cash-and-shares offer for TNS, which was tabled last month.
The report comes after TNS last night posted a defence document to shareholders, explaining in detail why the board rejected WPP's hostile bid.
Reasons given included TNS's position as a market leader, its significant investment in the internet, strong performance in 2007 and the fact that previous acquisitions in the sector have valued target companies substantially higher.
David Lowden, TNS chief executive, told the Financial Times that attempts to find more potential bidders have stalled because of a general reluctance to challenge WPP's Sir Martin Sorrell.
Lowden said: "In general people see the strength and value of TNS but they also see in WPP somebody with a very strategic reason to buy TNS and perhaps the ability to increase their price. A lot of people don't want to get into a bidding situation."
Lowden told the FT that TNS needs to consider "WPP and GfK from an equal standpoint", appearing more open to WPP than he had in the past.
He added that he believed TNs's greatest value could be secured as an independent business.