The news comes as the US food giant announces plans to sell under-performing brands including its Bird's Custard, Dream Topping and Angel Delight dessert ranges.
The company is looking to focus more heavily on its so-called "power line" brands, such as Kenco, Terry's chocolate and Philadelphia cheese.
Kraft has approached agencies directly. A mixture of roster and non-roster shops are competing for the brief. The pitch is being overseen by Carole White, who works within the marketing communications department at Kraft.
Six agencies pitched last week and the company is now looking to select a shortlist of three to go through to the final stage of the process.
Kraft's coffee portfolio in the UK includes the Mellow Bird's, Kenco, Carte Noire, Maxwell House and Cafe Hag brands. In other product areas it owns brands such as Oreos, Toblerone and Ritz biscuits.
A spokesman for the company declined to provide any further details.