"Apple and Hyundai are in discussions but they are at an early stage and nothing has been decided," Hyundai said in a statement without saying what the talks were about.
In a regulatory filing issued later, the automaker said it was "getting requests for cooperation on joint development of autonomous electric vehicles from various companies", without identifying any of them.
Apple declined to comment.
An Apple-branded car could be a big challenge to electric vehicle (EV) market leader Tesla Inc. It remains unclear who would assemble such a car, but analysts have said they expect the company to rely on a manufacturing partner to build vehicles.
"We continue to strongly believe Apple ultimately announces an EV strategic partnership in 2021 that lays the groundwork to enter the burgeoning EV space," Wedbush analysts said in a note.
Hyundai and Apple already work together on CarPlay, Apple's software for connecting iPhones to vehicles from a variety of automakers.
"Apple outsourcing car production to Hyundai makes sense, because (the Korean firm) is known for quality," said Jeong Yun-woo, a former designer at Hyundai and a professor at UNIST in South Korea.
"But I'm not sure whether it is a good strategy for automakers to be like the Foxconn of Apple as automakers face risks of losing control to tech firms," he added, referring to the Taiwanese contract manufacturer's supply contract with Apple on iPhones.
Analysts said Apple may be interested in using Hyundai's electric car platform and facilities to cut costs to develop and make vehicles.
"Apple could see Hyundai as an ideal partner, because when it comes to legacy U.S. automakers, they all have strong union, which Apple would like to avoid," said Kevin Yoo, an analyst at eBEST Investment & Securities.
"Moreover, their (legacy U.S. automakers) labour cost is much higher than that of Hyundai, which often plays a big role when it comes to car production."
A tie-up with Apple would be a major boost to the automaker, whose global sales last year fell more than 15% as the pandemic took a toll on demand.
A longtime champion of rival hydrogen fuel cell cars, Hyundai recently increased bets on battery-powered electric cars, a move welcomed by investors eyeing the recent success of Tesla.
The South Korean company, which sources batteries from SK Innovation Co Ltd and LG Chem Ltd and others, is expected to launch its first car based on a dedicated electric car platform known as E-GMP early this year.
Hyundai does not have dedicated electric car factories in the United States and it may have to gain consent from its powerful union in South Korea were it to seek to build EVs overseas, analysts said.
Shares in Hyundai Motor jumped as much as 24.8%, hitting a more than seven-year high of 255,000 won, while auto parts maker Hyundai Mobis Co Ltd jumped nearly 30%. Kia shares jumped some 14%.
Battery makers also gained ground, with SK Innovation up 7%. The broader KOSPI market was up 2.8% as of 0336 GMT.
(Reporting by Heekyong Yang and Hyunjoo Jin in Seoul and Stephen Nellis in San Francisco; Editing by Sayantani Ghosh and Kenneth Maxwell) ((Heekyong.Yang@thomsonreuters.com; +82 2 6936 1470;))