"This is just speculation and we won't comment one way or the other," a spokesman said.
Cordiant has been looking for a new senior executive, to fill either the chairman or the chief executive slot, since early this year when Maurice Saatchi, founder of Cordiant's predecessor company, Saatchi & Saatchi, left following a boardroom dispute.
Charlie Scott, acting chairman, said at the company's annual meeting last month that the "search for a new senior executive was proceeding well," a comment which the company spokesman repeated yesterday. He refused to provide further details about the search.
One prominent City executive turned the job down four months ago, reportedly after reviewing the company's balance sheet.
But a US executive such as Mr Miles might help Cordiant improve its reputation in a key market.
He has considerable expertise in consumer businesses, heading Philip Morris' food operation Kraft General Foods before rising to chairman.
Mr Miles left the company last year, when his proposal to divide food and tobacco operations was rejected by the board
In 1993, Philip Morris, under Mr Miles' leadership, ranked 11th among best performing companies, with a return to shareholders of 33.7 per cent. His pay was $11.4m (pounds 7.6m). Mr Saatchi left Cordiant after disputes over his demand for a pay package said to be worth pounds 6m.