Hertz shares climbed on Monday afternoon after news that Apple will work with Hertz on a small group of self-driving vehicles.

Sources familiar with the situation told CNBC that Apple is leasing six cars from a Hertz subsidiary for autonomous software testing. The cars are Lexus SUVs, according to Bloomberg, which previously reported the news.

Hertz shares spiked more than 13 percent at the close. Shares of Hertz also saw a small pop earlier in the day, after Alphabet and Avis announced a similar partnership with 600 vehicles.

Apple was not immediately available to comment on the report. Hertz declined to comment.

Apple CEO Tim Cook has called self-driving cars the "mother of all AI projects." "We're focusing on autonomous systems," Cook told Bloomberg in a previous interview.

Last month, Goldman Sachs analyst Stefan Burgstaller predicted that companies such as Hertz and Avis could enter the fleet management business as autonomous technology becomes more popular. Hertz and Avis could help ride-hailing companies, for instance, avoid owning as many physical cars, and could use their network of locations across the country for distributing the cars.

"They have experience in financing, buying, and reselling large numbers of vehicles, and have the real estate and physical urban presence to maintain, clean, and potentially (in an electric car context) run fleets," Goldman's analysts wrote in a research note. "Their current relationship with [manufacturers] is a symbiotic one: they acquire (cheaply) cars from [manufacturer]s, thus absorbing excess inventory. Car rental companies are likely to be willing participants in autonomous fleet management joint ventures or partnerships."

At least one other person on Wall Street was also betting on the car-rental industry: Hedge-fund legend Carl Icahn, whose firm owns nearly 35 percent of Hertz's outstanding shares, according to FactSet. Still, even with a double-digit gain on Monday, Hertz shares have fallen nearly 80 percent over the past year.

— With reporting by CNBC's Josh Lipton and Sally Shin.