The situation appears to be fluid; HP’s (HPQ) board plans to meet this afternoon. When reached for comment, an HP spokesperson decline to say anything about the matter. HP’s stock jumped on the news, up around 8% to 24.24.

The move would come at a pivotal time for HP, which has struggled to find a path forward. In mid-August, the company announced a vast planned overhaul of its business, agreeing to buy software maker Autonomy Corp. for $10.3 billion, canceling its TouchPad tablet and deciding whether to sell or spin-off its hardware division. The plan, in other words, called for the unraveling of the much-debated 2002 merger with Compaq Computer that helped turn HP into a technology behemoth.

Since taking over in November 2010, Apotheker has faced his share of reversals. A mere five months before announcing the latest plan, he had touted the company’s WebOS tablet operating system and promised it would ship with every Hewlett-Packard computer as well as a robust line of phones and tablet computers. In August, he pulled an abrupt about-face, announcing the cancellation of HP’s TouchPad tablet and the effective discontinuation of WebOS, which it got as part of a $1.2 billion acquisition of Palm last year.

Such moves might have been expected given Apotheker’s resume. In putting the former CEO of German software giant SAP (SAP) in charge, HP’s board effectively asked an executive with enterprise software expertise to go toe-to-toe in the low-margin PC business, not to mention a high-risk play to outflank Apple (AAPL) in smartphones and tablets. Apotheker’s moves to divest in both businesses came when PC sales slowed and the tablet failed to catch on.

What would HP get in Whitman? A seasoned executive with a long history in Silicon Valley — not to mention one familiar with the company. Whitman, 55, has been an HP director since early this year. After stints at Bain & Co., Disney (DIS), Procter & Gamble (PG) and Hasbro (HAS), Whitman was eBay’s president and CEO from 1998 until 2008. She transfored the tiny e-commerce startup with just 30 employees and $4.7 million in revenue into a giant with some 15,000 employees and almost $8 billion in revenue. (Whitman was Fortune’s Most Powerful Woman in Business in 2004 and 2005.) She eventually left, making a hard-fought but failed bid to become California’s governor.

Pressure is mounting on HP’s board to get something right. Before today’s news, its stock has been hammered, down over 40% from the beginning of the year. HP was widely criticized over the 2010 departure of former CEO Mark Hurd amid a scandal involving a personal relationship with a company contractor. (Hurd is a co-president at Oracle (ORCL).) Now, Apotheker’s tenure looks slated to barely outlast his 10-month run as CEO of SAP, which ended amid clashes with German unions and declines in revenue. As the board meets, HP’s long string missteps is surely foremost in mind.