WPP is hoping to thwart the planned TNS-GfK merger and went hostile with its bid after TNS rejected four friendly approaches from the marketing services group.
The group issued a brief statement in which it said: "WPP announces that the offer document containing the formal offer for the entire issued and to be issued share capital of TNS is being posted."
However, German rival Gfk advised TNS investors to sit tight while it continued to explore its own possible takeover bid for the firm.
GfK said in a separate release: "GfK is continuing to actively pursue an all-cash offer for TNS and discussions in relation to this possible offer are progressing positively.
"GfK therefore urges TNS shareholders to take no action in relation to WPP's offer for TNS at this time."
However, GfK went on to say that "no assurance can be given that an offer will be made".
Gfk and TNS had ditched their plans for a nil premium merger last month after WPP launched an unsolicited offer that valued TNS at £1.082bn.
If WPP's bid is successful, it will sell the television-monitoring arm of TNS, which measures TV and radio audiences in 25 countries, the Sunday Telegraph has reported.
TAM (Television Audience Management) is in direct competition with WPP's own audience measurement services operated by Millward Brown, which measures audiences in more than 30 countries.
The option to sell TAM, which is revealed in the offer document sent to TNS shareholders, has been made to allow WPP to get a possible acquisition of TNS through regulatory hurdles.
Without such a deal, WPP may need to spin off some of its existing operations to get approval from the European Union. The put option has been made for a maximum of £92m.