Insiders said directors at the financial PR firm were becoming increasingly dismayed at parent Cordiant's financial performance and were considering a possible MBO after Bungey's departure next April.
Cordiant, which declined to comment, has seen a troubled period in recent months - last week it was named the most undervalued stock in the media sector by Numis Securities and in September saw a group revenue slump of nearly ten per cent to £277m.
FD chief Charles Watson this week denied reports that a group of directors - said to include himself and non-executive chairman Tony Knox - were launching an imminent MBO bid.
He said they were 'not currently' in discussions with Cordiant over an MBO and denied that approaches had been made to the Cordiant board, led by outgoing CEO Michael Bungey.
Speculation suggests Cordiant would be reluctant to sell FD International because the PR network is one of the group's more profitable operations.