The tech giant wants to open a flagship store on the Paris avenue that draws millions of tourists and locals alike every year.
The store on the prestigious avenue, where top brands from around the world jostle to showcase their products, would bring to four the number of outlets the California-based company has in and around the French capital.
News of the possible new store comes on the day that Apple holds its annual autumn product launch event in San Francisco, at which it is expected to unveil an updated iPhone, new features for Apple TV and a possible expansion of the iPad line.
Le Figaro newspaper said Apple was in “advanced negotiations” with the owners of number 114 on the Champs Elysées to rent the entire 6,000-square metre, multi-storey building which also has underground parking for 110 cars.
But the shop would not open before 2018 as Apple would have to wait for the the current occupants' leases to expire.
The company did not immediately reply when contacted by The Local to seek confirmation of its reported plans for the new store.
There are currently two Apple stores in Paris - one next to the Opera house and a second in the underground shopping mall by the Louvre museum. And there is a third store in the business district in the Paris suburb of La Défense.