GE and Uber declined to comment.
Immelt, 61, is scheduled to step down next week from the CEO position at GE that he's held since 2001. John Flannery, a 30-year GE veteran, will take over, with Immelt remaining chairman until the end of the year.
Immelt embraced Silicon Valley in recent years, with the launch of a digital division in 2015 that he said could make GE a top 10 software company by the end of the decade. He has tried to bring startup strategies to the manufacturing behemoth, and GE even adopted the slogan "the digital industrial company."
But GE's shares fell by about a third during Immelt's tenure as he struggled to win the accolades bestowed on his predecessor, Jack Welch.
While Immelt was praised for dramatically reshaping the manufacturer, including shedding the bulk of its volatile finance business, he faced criticism for cutting shareholder dividends in 2009 and overpaying for some acquisitions.
Investors in the privately held ride-hailing company have lodged their own complaints against Kalanick, for constraints on their stock and questionable acquisitions. The former CEO made it extremely difficult for anyone to sell their stakes and paid US$680 million in stock for autonomous trucking startup Otto, a deal that soon led to a trade secrets lawsuit from Alphabet's Waymo.
The investors who pressed Kalanick to resign, led by venture capital firm Benchmark, cited the suit among the legal risks he helped put the company in during his tenure, people familiar with the situation have said.
The new chief will inherit a long list of other challenges, many of which have been festering for years but came to a head in recent months.
Uber's fiercely capitalistic, Ayn Randian sensibilities created a brand that's hard to love and gave opportunities to more approachable alternatives, such as hometown rival Lyft Politics became a liability when Kalanick joined US President Donald Trump's business advisory council, prompting a boycott.
Uber went through an internal crisis this year after allegations of sexual harassment and discrimination by employees. The company hired law firms to investigate and fired more than 20 workers as a result. The US Justice Department has introduced a separate probe into Uber's use of software called Greyball to help drivers evade law enforcement officials.
Still, Uber has the potential to become a once-in-a-generation business. Gross bookings in 2016 were US$20 billion. Those numbers have been growing ever larger this year, while losses shrink. And there are still investors out there who have expressed interest in climbing aboard. SoftBank Group has discussed taking a stake.
But Kalanick's presence will loom large over the next CEO. The 40-year-old has spent much of the past few weeks angling to retain influence in management of the company he helped start in 2009, people familiar with the matter said. He may eventually seek a new role for himself inside Uber, the people said.
Kalanick is one of five Uber directors on the subcommittee managing the CEO search. The others are Benchmark partner Matt Cohler, media mogul Arianna Huffington, Nestle SA's Wan Ling Martello and TPG's David Trujillo.
Cohler saw Whitman, 60, as a favorite before she withdrew, people familiar with the matter said. The board had considered her for a role at Uber prior to Kalanick's departure, possibly as a director, the people said. But Kalanick viewed the idea as an attempt to undercut his power, one of the people said.
He's also disinclined to take sides on any issue with Cohler, who helped push for Kalanick's resignation last month.
Like Immelt, Whitman has the kind of extensive business experience Uber is looking for. As CEO of EBay, she built the upstart into an e-commerce giant over a decade that saw a dot-com boom and bust before online shopping became a global way of life. EBay allowed anyone to sell items over the internet, much as Uber enabled anyone to become a driver for hire.
Whitman ran unsuccessfully in 2010 as the Republican candidate for California governor. At HP, she decided to split the technology pioneer in two. She stepped down as chairman of HP on Wednesday but said Thursday that she's "fully committed" to staying as CEO of HPE.
While Uber has recently hired an independent director, brand chief and strategy head, Uber's next CEO will need to find plenty more help.
The company has said it wants a chief operating officer, more independent board members and an outside chair. It also needs to hire finance and marketing chiefs, as well as a general counsel.
As the executive search continues, Uber is shedding some of the relics of Kalanick's presence inside headquarters. It has already renamed the War Room as the Peace Room. On the fifth floor, the names of conference rooms were selected, at Kalanick's direction, from the pages of science-fiction novels and movie scripts -- Galactic Empire, from Star Wars, and Hari Seldon, a mathematician from the "Foundation" book series who could predict the future. Those are being replaced with a more corporate alternative: names of countries where Uber operates.
