One of Immelt's earliest and strongest supporters on the board is Arianna Huffington, said sources, but he is also the top choice of several directors. Others still undecided — including Benchmark, which has weakened its status because of the lawsuit and ensuing publicity — have become convinced that Uber needs to hire someone who can quickly deal with a number of pressing and problematic issues and consider Immelt fully capable of handling that well.
"We know it is never going to be a perfect choice, but everyone is becoming exhausted," said one person close to the situation. "We need someone with the skills to move us along."
That includes dealing with the recruitment of numerous top execs in Uber's thinned ranks, worsening morale among employees, a need to diversify and expand its board, a detoxification of its culture and numerous legal and regulatory messes that have cropped up under Kalanick's tenure.
And, of course, someone who can handle the obstreperous Kalanick. Benchmark is accusing him of a number of bad acts since he was forced out of his job, including meddling in the operations of the company. That one is true, although Kalanick has denied a number of other allegations.
While I could do the back-and-forth of the noisy accusations, suffice it to say: It's awkward, since both Benchmark's Matt Cohler and Kalanick are on the board.
And, also suffice it to say, such machinations are unlikely to faze an experienced CEO like Immelt, which is one of the attractions of him, said numerous sources close to the deliberations.
"He certainly is not someone anyone can push around easily, which is probably his best characteristic," said one source. "We all know Immelt's not the dynamic entrepreneur that Travis is, but he can certainly settle things down."
Another source added that Immelt is also a known quantity to investors and Wall Street, as well as among techies, which would help greatly when Uber prepares to go public in the coming few years. "Even if Uber sold itself, Jeff could handle that too," the source said.
Also critical is to stop the focus on Uber's corporate drama that continues to spin out of control, much of it self-inflicted. The Benchmark lawsuit against Kalanick appears to be the final straw and has been badly received by the board and the company employees, as well as by much of Silicon Valley.
Many feel it is time to stop the chest-thumping escalation. (You think?)
Immelt would also benefit from being the person to rescue Uber. He announced in June that he was stepping down as chairman and CEO of GE after 16 years, the last few under pressure from investors who were critical of him and the pace of change at the sprawling conglomerate.
Still, as the Boston Globe noted on his last day at GE recently, he certainly tried: "Immelt saw GE's future in the 'Industrial Internet,' essentially big machines made super-smart by deep and constant data-crunching. He jettisoned businesses that didn't fit his 'digital industrial' vision: NBC, appliances, financial services. Even the light bulb, the symbol of GE for decades, wasn't safe."
Indeed, I have done a number of interviews with Immelt over the years and he was much more fast-forward than most bigwig traditional corporate CEOs and definitely understands the impact of the digital juggernaut.
The main ding on Immelt is that he is not a Silicon Valley type and it is not clear if he would move here from the East coast, where he was located as head of GE. As I noted in another post, when Hewlett Packard Enterprise CEO Meg Whitman dropped out of the running (she was a Benchmark favorite):
Some are worried that — while he is obviously a very experienced manager — he lacks the entrepreneurial drive to take the company to the next level. In other words, he's too much a corporate suit and not enough a geek pirate. (Anywhere else but in tech, this is not seen as a bad thing, but here we are.)
To sum up: Immelt is not a woman exec, as some wanted for the job. But he is also not a tech bro, which is good thing and also a bad thing.
Like I said, here we are.
I have reached out to Immelt and others for comment.
—By Kara Swisher, Recode.net.
CNBC's parent NBCUniversal is an investor in Recode's parent Vox, and the companies have a content-sharing arrangement.