The company’s stock has fallen 47 percent, a loss of over $40 billion in the company’s market value, on Mr. Apotheker’s watch.

Investors liked the prospect of new leadership. Hewlett-Packard’s stock was up 6.72 percent Wednesday to close at $23.98. It was not clear, however, that Ms. Whitman could undo much of what Mr. Apotheker had done or for that matter whether H.P.’s board would want her to. Analysts say it would be difficult for the company to walk away from the Autonomy bid, though the board may be considering hanging on to the PC business.

Ms. Whitman, who ran eBay as it grew from a start-up to a major online retailer, left the company just as growth began to stall. She unsuccessfully ran for governor of California and was hired in March by Kleiner Perkins Caufield & Byers, a venture capital firm, as a strategic adviser.

The board conversations about Ms. Whitman are fluid, though, and might not result in her hiring, this person said. However, if Ms. Whitman were hired, she would most likely be a permanent, not an interim, replacement for Mr. Apotheker, said a person briefed on the board’s discussions who asked for anonymity because he was not authorized by the board to speak publicly. While she lacks experience running a technology company as complex and mature as H.P., the company’s board considers her communications skills and understanding of customers to be her strongest qualifications for the job, this person said. Ms. Whitman joined the H.P. board in January, several months after Mr. Apotheker was hired.