His exit, expected to be announced when the company reveals its half-year results on Friday 6 September, comes after investor unrest over the company's share price, which has almost halved in the past six months.
Bungey is believed to be ready to resign as the chief executive within the next six months, when he will hand over to David Hearn, the head of the Cordiant-owned Bates Worldwide network.
Charlie Scott, the Cordiant chairman who has also been the subject of criticism for the group's dismal performance, is set to increase the number of non-executive directors on the Cordiant board. This will include more Americans.
Cordiant will not comment on Bungey's fate but insiders say that the decision has been taken. However, there have been moves to dampen the speculation that Cordiant will try to address the effects of its earlier ill-judged spending spree, which included the expensive purchase of The Lighthouse Group, by disposing of all or part of its 77 per cent stake in the German network Scholz & Friends.
Meanwhile, Europe-based Bates managers are increasingly alarmed by the impact that Cordiant's plight and the serious account losses it has suffered - which include the Wendy's International and Hyundai business, sustained by Bates in the US - are having on their business.
"The Bates operation in the US has virtually collapsed and when that happens the rest of the network suffers, one source commented. "It is getting very serious because clients are identifying with Cordiant's problems when we're actually holding our own in a tough market."
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