The project is code-named Titan and the design resembles a minivan, according to the report.
The Cupertino, California-based company has assigned several hundred employees to the vehicle.
While a car may not ultimately result, some Apple executives have flown to Austria to meet with contract manufacturers of high-end cars, the report said, citing people familiar with the matter.
Apple already has expertise managing a vast supply chain and has technology that may lend itself to an electric car.
The company has long researched battery technology for use in its iPhones, iPads and Macs. The mapping system it debuted in 2012 can be used for navigation.
Last year, Apple also introduced CarPlay, a software system for automakers to use in its cars that integrates iTunes, mapping, messaging and other applications.
Read more: Tesla Connection: Musk also said Apple has been trying to poach Tesla employees, offering $250,000 signing bonuses and 60 percent salary increases.