However, Brian Marshal, an analyst from Gleacher & Co. who claims to have discussed the matter with Cook, told Barron's that Cook is staying put at Apple.
Apple didn't respond to a request for comment.
Cook is the head of Apple's global sales and operations, including end-to-end supply chain management, as well as global sales, services and support. As the head of Apple's Macintosh division, Cook also has experience working with resellers and suppliers in the channel.
Speculation that Cook might leave Apple to take the HP CEO position first surfaced in mid-September.
Other possible candidates to replace Hurd as HP's CEO include IBM's senior vice president and group executive for Systems and Software Steve Mills; former Cisco executive vice president and chief deployment officer Charlie Giancarlo, currently managing director at Silver Lake; Ned Hooper, Cisco senior vice president of corporate development and senior vice president of the consumer group; Juniper Network's CEO Kevin Johnson; and Jon Rubenstein, former CEO of Palm, which HP acquired for $US1.2 billion in April. Rubenstein was himself an executive at Apple before leaving for Palm.
The HP CEO position became available when Mark Hurd resigned as CEO of HP on August 6, after being found in violation of the company's Standards of Business Conduct, following the conclusion of a sexual harassment investigation.
Hurd allegedly went around HP's board to settle with the contractor who initially accused him of sexual harassment. He was also accused of failing to maintain accurate expense accounts and misusing company assets.