Hewlett-Packard’s Board of Directors met Wednesday to discuss the possible ouster of CEO Leo Apotheker less than one year after he was brought in to replace then-head Mark V. Hurd. Hurd was fired over discrepancies in his expense reporting, and his now co-president of Oracle, an HP competitor. Apotheker, who formerly held the title of co-CEO of enterprise software company SAP, has recently come under fire for his decision to kill off HP’s webOS division as well as for what some critics call his plan to transform HP from a consumer hardware company into an SAP clone.

Multiple media outlets including The New York Times and Wall Street Journal are reporting that former eBay head and California gubernatorial candidate, and current HP board member, Meg Whitman is a leading candidate to replace Apotheker. Whitman lost the Governor’s race to Jerry Brown and is now installed as a strategic consultant at heavyweight venture capital firm Kleiner Perkins Caufield & Byers in addition to her duties on HP’s Board of Directors. According to WSJ, Whitman may not be interested in the position and requests for comment were passed on from her camp to HP, who declined to comment.

Whitman’s twenty years at eBay saw the online auction house-cum-retailer grow annual revenues from $66 million to a whopping $7.7 billion, though she’s also still remembered for the company’s $2.5 billion acquisition of Skype in 2005. That deal later involved a $1.4 billion write-down and was roundly considered a failure. After leaving eBay, Whitman spent a record $178.5 million on her bid for California’s highest political office.

While Whitman has no experience running a hardware company, there’s no denying eBay’s growth during her tenure. Then again, the company’s standing has slipped in recent years, and financial industry media outlets like Fortune are already sending out warning signals regarding her possibly taking over HP’s helm:

Whitman does not necessarily have the best reputation for respecting the independent role of a board and avoiding conflicts of interest in the past. She stepped down from the Goldman Sachs board in 2002 amid allegations that, she was allocated pre-IPO shares by Goldman Sachs (GS) which netted her $1.8 million in profits as a result of eBay (EBAY) doing investment banking business with the investment bank.

WSJ’s Shira Ovide goes Fortune a step further, wondering outright if HP has “The Worst Board Ever?”

The political particulars of megacorps and their Directors notwithstanding, HP would be wise to think long and hard about the best choice to replaceApotheker if, in fact, they’re planning on playing another round of musical CEO chairs. HP’s endured more than one scandal in recent memory, and shareholders can’t be too happy about last April’s $1.2B acquisition in Palm having literally gone nowhere before being thrown out with the trash a few weeks back. HP’s stock closed up 6.72% Wednesday at 23.98/share but is still more than 50% off its 52-week high of 49.39.