Hertz shares were up 13.5 percent at $10.82, while shares of Apple were slightly down.
Apple is renting Lexus RX450h sport-utility vehicles from Hertz's Donlen fleet-management unit, according to the Bloomberg report, citing documents released recently by the California Department of Motor Vehicles. (bloom.bg/2tdqm8n)
The iPhone maker is concentrating on technology for self-driving cars, Chief Executive Tim Cook said earlier this month in an interview with Bloomberg.
Hertz declined to comment, while Apple did not immediately respond to a request for comment.
Alphabet Inc's (GOOGL.O) self-driving car unit Waymo announced a similar partnership with Avis Budget Group Inc (CAR.O), earlier on Monday, to offer fleet support and maintenance services for its fleet of autonomous vehicles.
Reporting by Rishika Sadam in Bengaluru; Editing by Shounak Dasgupta