Uber appeared to have found a new hand to steady the wheel at the smartphone-summoned ride service, which has skidded from one controversy to another.
"Nothing has been yet finalised, but having extensively discussed this with Dara I believe it is his intention to accept."
Uber and Expedia did not respond to AFP requests for comment.
Khosrowshahi is known as an experienced top executive, willing to speak his mind and to advocate for women getting equal pay and leadership opportunities.
His most recent Twitter post criticizes US President Donald Trump for his response to a white supremacist rally that turned deadly in Charlottesville.
"I keep waiting for the moment when our Prez will rise to the expectations of his office and he fails, repeatedly," Khosrowshahi said the tweet, which included a link to a story about the Trump controversy.
Born in Iran, Khosrowshahi immigrated to the United States with his family as a child and became a citizen here.
Expedia shares have climb more than five-fold during the 12 years Khosrowshahi has been in charge of the travel services internet firm.
Whoever takes charge at Uber will face challenges including conflicts with regulators and taxi operators; a cut-throat company culture, and board members feuding with investors over Kalanick.
Kalanick was the driving force behind Uber, taking a spur-of-moment idea and turning it into the world's most valuable venture-funded tech startup.
But his brash personality and freewheeling management style made him a liability as well as an asset to the global ridesharing giant, and in June he stepped down as chief executive.
Kalanick, who turned 41 this month, frequently recounts how the idea behind Uber was born, when he and a colleague were attending a technology conference in Paris in 2008 and failed to find a taxi on a cold night.
Uber now operates in hundreds of cities and more than 80 countries.
But the hard-charging style that helped Uber succeed also made Kalanick a target for critics.
He has borne responsibility for allegations of nasty workplace tactics and covert use of law enforcement-evading software.
Dents to Uber's image include a visit by executives to a South Korean escort-karaoke bar, an attempt to dig up dirt on journalists covering the company, and the mishandling of medical records from a woman raped in India after hailing an Uber ride.