PALO ALTO, California ( TheStreet) -- HP's ( HPQ - Get Report) search for a new CEO may be getting tougher. Reuters reports that the tech giant recently approached two senior executives at arch-rival IBM ( IBM - Get Report) about the role, but has been turned down.

HP reached out to IBM software chief Steve Mills during the early stages of the company's CEO hunt, according to Reuters, which cites two unnamed sources with knowledge of the approach. Mills, who is one of IBM's heaviest hitters, reportedly rebuffed HP.

Reuters reports that Virginia Rometty, senior vice president for IBM's sales, marketing and strategy, was also targeted, but similarly declined HP's approach.

HP's quest follows the departure of former CEO Mark Hurd amid an expenses scandal that sent shockwaves through the tech sector. Hurd, who took the helm at HP following the departure of Carly Fiorina, is credited with turning the tech giant's fortunes around, and there has been intense speculation about who will replace him.

Ann Livermore, head of H-P's $54 billion enterprise business, has been touted as potential successor to Hurd, along with HP storage chief Dave Donatelli. Todd Bradley, the VP who runs HP's personal computer business, and the company's printer boss Vyomesh Joshi have also been mentioned as likely internal candidates.

There has also been chatter linking Cisco ( CSCO) executive Ned Hooper with the vacant HP hotseat, as well as Apple ( AAPL - Get Report) COO Tim Cook, although this seems highly unlikely given Apple's continued growth and Cook's esteemed status as Steve Jobs' right-hand-man. Widely regarded as the company's heir apparent, Cook took over the running of Apple during Steve Jobs' recent medical leave and has helped grow Apple to its current $259 billion market cap.

Cook reportedly described the rumor linking him to HP as "ridiculous" earlier this week.

HP shares dipped 33 cents, or 0.78%, to $42.20 on Thursday, mirroring the broader fall in tech stocks that saw the Nasdaq slip 0.76%.

--Written by James Rogers in New York.

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