Under the proposed deal, M&C Saatchi would retain a stake of just under a quarter of Walker Media, which has been valued at about £46m, according to people close to the talks.
The companies hope to complete the transaction as soon as next week, the people said.
However M&C Saatchi said in a statement on Thursday: “There can be no certainty that an agreement will be reached and a further announcement will be made in due course.”
Walker Media, whose clients include Marks and Spencer, Boots, and KFC, operates only in the UK.
Publicis, which is merging with US rival Omnicom, plans to fold Walker Media into ZenithOptimedia, its media planning and buying business.
Ian Whittaker, media analyst at Liberum Capital, said the acquisition made sense for both M&C Saatchi and Publicis because “media buying and planning is the one area that you need scale”.
Media buying agencies increasingly need to invest substantial amounts of money in new technology to keep up with the growing complexity of digital marketing and advertising.
Walker Media was founded in 1998 by Christine Walker and Phil Georgiadis as a 50/50 joint venture with M&C Saatchi. In the years that followed, M&C Saatchi increased its stake in the business to more than 90 per cent.
Shares in M&C Saatchi were up 5.5 per cent to 341.25p by noon on Thursday in London, giving the company a market capitalisation of £232m.
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