Fortune magazine, in a news release trailing a report due to appear in the 28 December issue, described the shake-up as a corporate putsch.
The magazine named the former Mobil chairman Rawleigh Warner as leader of the coup, adding that Mr Robinson, 57, chief executive officer for more than 15 years, would step down as soon as a successor was found.
But later on Saturday, Mr Warner released a statement denying that the succession process was anything other than orderly.
According to Fortune, Mr Robinson had the support of the American Express board right through last year's poor performance at the cornerstone unit that includes the American Express card and travellers' cheques.
But as losses mounted, Mr Warner, who at 71 is due to retire from the board, 'must have felt that it was time for him to make a difference'.
American Express, with assets of dollars 146bn and revenues of dollars 25.7bn, ranks number two on the Fortune Service 500 list of the largest diversified financial companies.
Its credit card and brokerage business has been hit by fierce competition, hurting both profits and the price of its stock. Low profitability, Fortune says, has led to the elimination of 6,500 jobs at the company since 1991.
Harvey Golub, former head of Amex's IDS Financial Services group, is rumoured to be among the top contenders for the post.
Mr Golub, 53, took charge of the card division and became president of the company last year.Reuse content