The US regulator, the Federal Trade Commission, has been examining the deal, but is yet to announce whether it is to launch a formal investigation.
Speaking to reporters at the World Economic Forum on Europe in Brussels yesterday 10 May), Sorrell said: "It [a regulatory investigation] should be rigorous."
The WPP chief executive criticised the FTC's approval of Google's $3.1bn acquisition of online display advertising company DoubleClick in 2008.
"I don't think in the case of DoubleClick it was deep enough and strong enough," said Sorrell.
The FTC concluded that the DoubleClick deal was unlikely to substantially lessen competition.
Google, which agreed the AdMob deal in November last year, has previously said it is "confident the FTC will conclude that the rapidly growing mobile advertising space will remain highly competitive after this deal closes".
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