Last week Sorrell's WPP Group warned TNS shareholders it was not going to increase its £1.1bn bid and that its offer was final.
At the same time it revealed acceptances had climbed from 34% to 43%. Valid acceptances of the offer now stand at 60.86%.
WPP has taken up its right to extend the offer until 3pm on Wednesday.
If Sorrell wins 75% of acceptances, he can delist TNS from the stock market.