"There's not been a company ever turned around by the fifth CEO on the job," Chambers said in a wide-ranging interview with Reuters, referring to HP's management history.
Whitman replaced the harshly criticized Leo Apotheker at the helm of HP almost exactly one year ago in a bid to restore investor confidence in the iconic Palo Alto company.
Chambers said there was potential for HP, the world's No. 1 personal computer maker, to grow in market transitions to cloud computing and the move from PCs to tablets, but the company may not be able to catch up. Cisco and HP compete in a number of areas, such as networking equipment.
"Its a tough hand to play, but clearly as a competitor I like competing against that hand, and we are going to try and accelerate while they are struggling," Chambers said.
HP has continued to
Chambers softened his comments by saying that he is a "huge" Whitman supporter, pointing to his backing of her unsuccessful run for governor of California in 2010. He said he believes she took the chief executive job at Hewlett-Packard in part because of her deep respect for the culture of Silicon Valley.
"She did it, I believe, because she cares about the Valley so much and HP is an integral part of the Valley," Chambers said.
Speaking to the shared interest among technology company CEOs in preserving Silicon Valley's distinct culture, Chambers related an experience he had during his early days at San Jose-based Cisco with another HP boss, Lew Platt.
Chambers said that when he first got to "the Valley," he didn't know anything about it, so he asked Platt to teach him about the culture.
"He met with me, and I asked for the next quarter and he met with me again; three years later we met every quarter," Chambers recounted. "He let me bring my team and he would bring his team, after three years we were on a roll."
Years later, when Chambers asked Platt what was behind his generosity he replied, "John, this is what our culture is about."