The company is thought to be lining up a meeting of the full board as soon as all directors, including its non-executives, are available.
The intention to speed up the decision-making process followed a five- hour board meeting at M&S's head office in Baker Street, London, on Monday which included some of the non-executive directors.
That came after Sir Richard Greenbury, M&S chairman, cut short a combined business trip and holiday in India to fly back to help resolve the crisis.
M&S originally planned to make an announcement about the succession in May after it had completed its strategic review. However, the intensity of the speculation over Sir Richard's successor means it is highly unlikely that the company will be able to wait that long.
The company has also clamped down on speaking to the media in order to try to stem the tide of speculation.
It is thought that several non-executives support Sir Richard's plan that Peter Salsbury, the managing director in charge of general merchandise, should become chief executive, with Sir Richard moving to the chairmanship. It is possible that Sir Martin Jacomb, chairman of Prudential, which is M&S's biggest institutional investor, may support a different approach.
Several other M&S directors below managing director level are believed to favour a more radical change at the top. This would indicate support for Keith Oates, deputy chairman, who has made a direct approach to the non-executives to advance his candidacy as either chairman or chief executive.
Chris Littmoden, head of the US operations, remains an outside candidate. There was a feeling yesterday that Lord Stone, managing director in charge of food operations, might emerge as a potential compromise candidate, but this was discounted by some insiders as "unlikely".
Analysts expressed surprise yesterday that M&S shares had risen as the leadership battle intensified. Yesterday they closed 18p higher at 436p.