The new handsets are still in development and plans haven't been completed, Bloomberg said citing the person, adding Apple probably would release them in the third quarter of next year.
Meanwhile, Natalie Kerris, a spokeswoman for the Cupertino, California-based technology company, declined to comment.
Earlier in October, Samsung Electronics Co Ltd launched the world's first smartphone with a curved display, a variant of the Galaxy Note which moves the Asian giant a step closer to achieving wearable devices with flexible - even unbreakable - screens.
Also, only days ago, rumours were swirling that Apple was looking into building bigger tablets.
If the latest rumours are to be believed its long-time manufacturing partner Foxconn was currently testing giant-sized iPads ahead of a spring 2014 launch.
Moreover, a number of analysts believe that Apple is set to release a hybrid or convertible computing device that looks like a notebook but runs iOS rather than the company's desktop operating system.