Amazon is threatening Google and Facebook's dominance of the digital ad space, Martin Sorrell told CNBC at the World Economic Forum in Davos on Tuesday.

The CEO of WPP, the world's largest ad company, explained why he saw a growth trajectory ahead for the American e-commerce giant's ad business.

"Amazon threatens Google in two ways. One is search — 55 percent of product searches in the United States emanate from Amazon. So that's a big question for Google," Sorrell said.

Still, Amazon's market share doesn't come close to the duopoly of Facebook and Google. The two tech and media behemoths control about 75 percent of the digital ad space, Sorrell said.

"Amazon's advertising platform itself — Google has about $100 billion in advertising, Facebook about $40 billion. Amazon has a fairly paltry pimple really, $2 billion or so, but growing quite quickly."

The advertising tycoon said he spent about $5 billion with Google last year, roughly $2 billion at Facebook and $200 million on Amazon on behalf of WPP's clients.

"This year we'll be ramping up to about $300 million," Sorrell said, "so it's growing, but it's at a very small scale."