Deadline reports that the comedy stars have signed up to act in the movie, which will be filmed this autumn.
Funded by Sony Pictures International Productions and Film4, the currently untitled project is set to be a satirical take on the world of the super wealthy.
Coogan will reportedly play "a ruthless, perma-tanned and self-absorbed retail clothing billionaire", a character description which appears to share some links with Philip Green, the Arcadia Group chairman who owns chains including Topshop and Burton.
Meanwhile, Mitchell looks set to take on the role of "a mild-mannered journalist hired by Coogan's character to chronicle his life story."
The project has previously gone under the working title of Greed, but the trade publication says this name will not now be used. When first announced, Sacha Baron Cohen was linked to the production, but it would appear he is no longer involved.
Coogan will next be seen in Stan & Ollie, the film about Laurel & Hardy on their 1953 UK tour. Set to be released in January, it stars Coogan as Laurel with John C. Reilly as Hardy. The comedy star has also filmed a new Alan Partridge series for the BBC - This Time With Alan Partridge will be on TV early next year.
Further details about this new Winterbottom film are expected to be revealed nearer to filming. The production schedule would suggest that it'll be in cinemas in 2019.
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