Private equity firms Bain Capital, Apollo and Platinum have made it through to the final stages of the auction along with a fourth undisclosed bidder, the sources said.
The world's biggest advertising company held management presentations with the bidders on May 15, one of the sources said, and aims to wrap up the process towards the end of June.
Private equity investors have about four weeks to carry out in-depths checks on Kantar before submitting their final bids, this source said.
WPP declined to comment while Bain, Apollo and Platinum were not immediately available.
The auction, led by Goldman Sachs, kicked off last year drawing interest from a broad spectrum of financial investors including European private equity houses CVC Capital Partners and Permira.
Kantar generates about 15% of WPP's overall sales and provides brand and marketing communications research for some of the world's largest advertisers.
The business is valued at about 3.5 billion pounds, representing a multiple of seven to nine times its earnings before interest, tax, depreciation and amortization (EBITDA) of $550 million, two of the sources said.
Some investors have expressed concern over Kantar's business model which is being challenged by disruptive digital technologies.
The unit's underlying sales slipped 2 percent last year to 2.6 billion pounds with operating profits down 14 percent to 301 million.
The business has also traditionally weighed on the company's overall organic growth rates, a key measurement for the industry.
WPP new boss Mark Read has identified a Kantar sale as one way to bring in cash and help steer WPP back to growth.
While clients need access to data and customer insight, WPP does not need to own it outright, he believes.
Last year he pledged to spend 300 million pounds to restructure the group and bring it back in line with peers by the end of 2021.
(Editing by Alexandra Hudson)
By Pamela Barbaglia and Kate Holton