Hewlett-Packard’s (HPQ) board of directors is considering ousting CEO Léo Apotheker after less than a year on the job and replacing him with former eBay (EBAY) CEO and California governor candidate Meg Whitman, two sources familiar with the matter told this newspaper Wednesday.

Whitman could be brought in as an interim replacement for Apotheker at the Palo Alto tech giant, the sources said.

Bloomberg News and Wall Street Journal and AllThingsD reporter Kara Swisher also credited unnamed sources in reporting the same information Wednesday, though Swisher cautioned that Whitman’s appointment was not a sure thing.

The New York Times reported that HP’s board planned was meeting Wednesday to discuss the possible move.

Investors appeared to be appeased by the proposed action, as Hewlett-Packard’s stock price jumped after the reports surfaced. By 10 a.m. PDT, HP shares were trading at $24.82, an increase of $2.35, or 10.5 percent, from Tuesday’s closing price.

Apotheker was named CEO 11 months ago to replace Mark Hurd, who was ousted from the CEO post after being accused of falsifying expense reports in a controversy that started with an allegation of sexual harassment by an HP contract employee. Apotheker was previously CEO at German software giant SAP, a position from which he resigned in early 2010 after disappointing results.

Whitman took the reins as president and CEO at eBay in 1998 and led it through its initial public offering and massive growth before leaving in 2008. In 2010, she won the Republican nomination for governor of California. She lost to Gov. Jerry Brown in the general election after spending more than $140 million of her own fortune in the quest to lead the state.

HP has been the world’s leading PC-maker for the past five years, after buying one major rival, Compaq, and overtaking another competitor, Dell, in the race for market share. But its business has been under increasing pressure, both from the introduction of such alternatives as the iPad and from competition with low-cost manufacturers that have forced HP to keep its prices and profits down.

Since taking over the top job, Apotheker has announced that HP will spin off its core personal-computer business, end its foray into the tablet business and purchase British software company Autonomy for $10.3 billion.

“This is about a transformation to position HP for a new future,” Apotheker said in announcing those changes last month. He vowed to build HP’s business in high-margin commercial tech sectors such as software, consulting and cloud computing services, in which information and services are delivered over the Internet.

After announcing the Autonomy deal on Aug. 18, Apotheker met with some customers and analysts to explain the decision. But he has kept a low profile recently, canceling an appearance at a tech industry conference and declining to give interviews, leaving board chairman Ray Lane and PC division chief Todd Bradley to explain the company’s strategy in numerous interviews and public appearances.

The day before Apotheker’s appointment as CEO on Sept. 30, 2010, HP stock closed at $42.04; at the close of trading Tuesday, the price stood at $22.47, a decrease of more than 46 percent in less than a year.

Contact Jeremy C. Owens at 408-920-5876; follow him at Twitter.com/mercbizbreak.