The South Korean car company initially said it was in the “early stage” of talks with the iPhone maker about a possible electric car partnership.
But hours later it backtracked and said it was talking with a number of potential partners without naming Apple.
Hyundai’s share price rose more than 20% when the tie-up was announced.
“Apple and Hyundai are in discussions but they are at an early stage and nothing has been decided,” it said in a statement which was later revised. Hyundai’s value shot up $9bn (£6.5bn) after the Apple announcement.
While an updated statement said it was talking to a number of companies about a possible electric car tie-up including Apple, a later version omitted the US tech firm.
Apple is known for its secretiveness when it comes to new products and partnerships.
Last month, news emerged that Apple was moving forward with self-driving car technology with a 2024 launch date.
The electric vehicle (EV) market is becoming increasingly competitive, with companies such as Tesla grabbing the headlines with its rapidly-increasing valuation. Tesla chief executive Elon Musk is now the richest man in the world, displacing Amazon founder Jeff Bezos.
Experts say an electric vehicle from Apple is still at least five years away.
They say pandemic-related delays could push the start of production into 2025 or beyond.
Hyundai has already been pushing into new technologies such as electric, driverless and flying cars.
Last month, it took a controlling stake in Boston Dynamics in a deal that valued the mobile robot firm at $1.1bn.
The company is also setting up a $4bn autonomous-driving joint venture with auto parts supplier Aptiv.
Both partners will invest $2bn, while Ireland-based Aptiv will contribute about 700 engineers and transfer patents and intellectual property to the venture.
Apple’s efforts to produce an electric car, known as Project Titan, have been on and off ever since plans were revealed in 2014.
There have been rumours over who would assemble an Apple-branded car as it may be difficult for the tech giant to manufacture them on its own.
Its rival Alphabet’s Waymo chose a factory in Detroit to mass produce its own self-driving cars.