Mr Zadesky was given permission to create a 1,000-person team to work on the car and cherry-pick employees from different parts of the company, the sources said. Many Apple employees who had been considering leaving the company have been persuaded to stay there to work on Titan.
An "automotive research lab" was reportedly established at a confidential Silicon Valley location outside Apple's main Cupertino campus at the end of last year.
The company has existing links with the car industry through its dashboard touchscreen system, CarPlay, which is being supported by manufacturers such as Daimler, Volvo and Volkswagen.
Technology industry commentators have previously dismissed the idea of an Apple electric car, pointing out that the company does not have its own facility capable of mass automobile production.
"It's one thing to draw pictures but it's a quantum leap to manufacture things, and Apple doesn't even manufacture," one industry insider told the Financial Times.
However, building a car plant would not be an obstacle for Apple, which is estimated to hold around $178bn (NZ $238bn) in cash. If Titan does come to fruition, it could rival the ground-breaking vehicles created by Tesla, the electric car manufacturer owned by PayPal billionaire Elon Musk.
Last week, someone claiming to be an Apple employee emailed the Business Insider website to say that the firm's latest project would "give Tesla a run for its money".