GM’s Stempel Reported to Be Stepping Down : Auto industry: The move could come within a month, but no successor has been chosen, company sources say.

The outsiders who control the General Motors Corp. board of directors want Chairman Robert Stempel to step down within the next month, but they are still debating who will succeed him, board and management sources said Tuesday.

The consensus that Stempel should go reflects the concern of the outside directors, who are not part of the company’s management, over the decline in the financial condition of the world’s largest corporation. It is not clear whether Stempel will fight to keep his job, but the directors have the power to remove him.

The board is also considering again the elimination of at least one of the company’s six automobile divisions, sources said. The current target is Oldsmobile, whose sales of 437,544 cars for the model year ended Sept. 30 are less than half of what they were in the same period for 1986. The board is also reviewing the company’s entire marketing strategy in light of GM’s slide.

GM next week is expected to announce an $845-million loss for the third quarter. The company, which lost more than $7 billion in its core North American auto operations in 1991, has not reported an overall profit since Stempel became chairman in August, 1990.

A GM spokesman denied Tuesday that directors were trying to remove Stempel.

Stempel was in Cleveland Tuesday talking to a group of minority auto dealers and could not be reached for comment.

However, other GM management and board sources insisted that a shake-up was in the works.

Board sources said the outside directors have grown increasingly unhappy with Stempel since last April, when they effectively stripped him of any operating power and demoted the person he had picked for president, Lloyd Reuss. The board named John F. Smith Jr. as president and assigned Reuss to the post of executive vice president.

Stempel’s role since then has been largely ceremonial, involving frequent meetings with outside groups, sources said. Even though he remains chairman, the board has been steered by John G. Smale, the chairman of the executive committee, who meets privately with Smith each month to set the agenda for board meetings.