Meg Whitman, the CEO of Hewlett Packard Enterprise, is still being pushed by Uber's biggest investor as a candidate for the company's open CEO position, according to two sources close to the matter.

Whitman publicly denied she wanted the job on July 27 when she tweeted, "Uber's CEO will not be Meg Whitman."

Tweet from Whitman

But two sources familiar with the CEO search process tell CNBC that Uber investor Benchmark is still telling people that she is a potential candidate, and that she has had conversations with Benchmark since her public statement. These people say that she is Benchmark's preferred choice.

Another person close to the situation says that Whitman's stance has not changed and she is not interested in the job.

Benchmark denied that it is now pursuing Whitman's candidacy for the Uber role, saying in a statement that it had not reintroduced her name for consideration.

Whitman's relationship with Benchmark goes back to the 1990s. Benchmark was an early investor in online retailer eBay, which hired Whitman as CEO in March 1998. The firm held a 22 percent stake in the company when it went public later that year.

One source told CNBC that both Whitman and former GE CEO Jeff Immelt -- whom Recode reported was the frontrunner in Uber's CEO race -- have previously spoken to all board members either on the phone or in person, an indication that both are being seriously considered.

The CEO search is taking place as a board battle rages over former CEO Travis Kalanick's future with the company. Earlier this month, Benchmark filed suit against Kalanick seeking to eliminate three board seats added when he was CEO, and to remove him from one of those board seats. In the filing, Benchmark alleged that Kalanick had attempted to conceal certain facts from the board, including allegations of widespread sexual harassment within the company and a possible legal conflict with Alphabet subsidiary Waymo over self-driving car technology.

Kalanick has as a "public and personal attack" without merit, and is seeking arbitration to resolve the dispute.