Mr Muirhead, who heads one of Saatchi's main agency networks in Europe, is believed to have the support of both Maurice Saatchi, the group chairman, and Charles Scott, the chief executive. And it is widely believed within the group that Mr Muirhead could soon clinch the coveted, but tough, Madison Avenue post.
Two weeks ago, the Independent on Sunday disclosed that Saatchi had warned its bankers not to expect any significant improvement in its performance until at least next year because of weak margins.
The problems, which stem from the loss of key US clients and a failure by the New York agencies to win big new accounts has fuelled a bitter power struggle between Messrs Saatchi and Scott.
Mr Kennedy was forced into retirement last month after only a year in the top job, after serious differences with Mr Scott over the US agency's performance. After 33 years with the group, he is to receive a pounds 4m pay-off from the company over the next few years. His annual salary amounted to nearly dollars 800,000 ( pounds 537,000) - higher than that of any of the group's main board directors.
Mr Muirhead, who has been with Saatchi since its early days, would be the second European executive to take charge of a US arm of the group in the past year. Michael Bungey, former European head of BSB Dorland, was appointed to similar post in the US to turn around the business there.
Mr Muirhead's position has been strengthened by few internal rivals for the job, although Saatchi could still bring in new blood from outside to bolster the US network. He also has a close working relationship with many of Saatchi's most important multinational clients, such as Toyota, the Japanese car maker, and Procter & Gamble, the detergents group.
However, it is unclear whether he would be based in the US and inherit Mr Kennedy's salary package.
In contrast to the group's US problems, its British agencies have held on to their market share. An annual survey published last week by Campaign, the trade paper, ranked its Saatchi agency as the biggest in the UK, with total billings up 16 per cent to pounds 264m. BSB Dorland, placed seventh, lifted billings by 10 per cent to pounds 159m last year.Reuse content