Apotheker took over from Mark Hurd, who left the company in August 2010 under a cloud following a sexual harassment investigation.
The HP board is said to have reacted following investor criticism of Apotheker's plan to migrate from hardware to focus on software and services.
The HP board is said to be planning to meet with a view to replacing Apotheker, with board member and former eBay head Meg Whitman the most likely candidate.
Such a move would not come cheap though, with some reports suggesting that removing Apotheker could cost HP as much as $33m (£21.3m).
As rumours of a change at the top began circulating (21 September), HP's share price rose from $22 to more than $24 per share on the New York Stock Exchange.
In the company's third quarter results released in August, its printing division added $6.1bn (£3.7bn) to the IT giant's $31.2bn net revenues, down 1% year-on-year.
Sales of its commercial presses came in at $1.3bn for the quarter ending 31 July, down 7% year-on-year and 10% sequentially, although hardware units rose 1%, and sales were marginally up for the nine months.
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