Sir Malcolm's position has been under threat since the company issued a profits warning last month - its first in 15 years.
WH Smith has already parted company with the managing director of UK retailing, Peter Troughton, who announced last month that he is leaving the company by mutual consent and the City has been expecting more changes at the top.
Yesterday Smith admitted that it was talking to a firm of search consultants about a new chief executive but said a search had not yet started. It added that Sir Malcolm would be leaving of his own volition and would remain in position for "at least nine to 12 months from now".
Under WH Smith's internal rules directors can retire at 58 and Sir Malcolm reached that age last August. The company says Sir Malcolm was thinking of leaving then but is now likely to stay on to help the group turn the corner.
However, City analysts and institutional shareholders doubt he will be around to oversee the group's rehabilitation. One institutional shareholder said: "We do not have a large holding but if we did we would support change at the top."
Another insider likened the Smith malaise to that of the Conservative Party: "Nothing will change unless you get a change right at the top."
There are also rumblings that the Smith family, which still accounts for around 10 per cent of the company's shares, are dissatisfied about the collapse of the company's share price and the departure of Mr Troughton. He is the son of a former Smith's chairman and is believed to be close to the Smith family. One observer said there was "a bit of family push" for change.
However the company denied there was any rift between the directors and the family, who are represented on the board by Philip Smith. "We are not aware of any growing dissatisfaction. There is no substance at all in any suggestions that family factions have been pressing for Sir Malcolm to go."
Any family pressure for change would be a big departure for WH Smith which has always been a conservative business, promoting from within. Sir Malcolm has been with the company for 32 years, including the last 15 as a director. His predecessor Sir Simon Hornby who retired last year, spent his entire working life with the company, including 12 as chairman.
As one City analysts said: "It's always been a highly in-bred company where a particular social class gets to the top."
The widespread belief is that the company is in desperate need of a senior external appointment to help the company battle against increased competition.
Last month's profits warning, which knocked 16 per cent of the company's share price, was blamed on difficult trading conditions, fewer shoppers on the high street and a shift away from high-margin products such as magazines.
The company has since announced a package of initiatives to restore the core Smith's chain to healthReuse content