The statement comes only a few months after the two companies were locked in a legal battle over self-driving technology. Waymo, owned by Google parent Alphabet, sought $1.8 billion from the ride-sharing startup, claiming Uber had stolen critical trade secrets. In the end, the two companies agreed a settlement which saw Waymo awarded 0.34 percent of Uber's equity -- around $245 million -- and given the guarantee that Uber would not use Waymo's confidential research in its self-driving cars.

Clearly, Waymo has the technology that Uber needs. "When we get back on the road, we have to be absolutely satisfied we're getting back on the road it in the safest manner possible," Khosrowshahi said, alluding to an incident in April where one of Uber's self-driving cars was involved in a fatal crash with a pedestrian. Since then, all self-driving operations have been halted.

This is not the first time the Uber boss has hinted at working with Waymo. However, should a partnership between the two go ahead, Uber's program could be up and running again by this summer. "Autonomous will be shared," Khosrowshahi said, adding that the two companies are "having discussions" about a future together. What that future will look like given their complicated history, however, remains to be seen.