Two models are planned for release in the latter half of 2014 which would feature larger displays with curved glass, the report said, citing an unnamed person "familiar with the plans" who did not wish to be identified as the details are not yet public.
Sensors that can detect different types of pressure on the screen could also be included in subsequent models, the person said, adding that with screens of 4.7 inches and 5.5 inches, the two new models would be Apple's largest iPhones.
If true, the report could mark the start of a new battle between the rival smartphone makers Apple and Samsung as they compete to dominate the global smartphone market . The companies have already been through a protracted court battles over alleged infringements of smartphone patents.
(Read more: Samsung 'Galaxy Gear' may ignite smartwatch wars )
In September, rival smartphone maker Samsung launched the Galaxy Note 3 -- which features a 5.7-inch display screen. In October, the Korean phone maker launched the Galaxy Round which has the same sized display and a slight horizontal curve .
A curved display essentially wraps around the device to cover the left and right edges so that if the phone is placed face down, text messages or stock tickers, for example, can be displayed along a side.
(Read more: Samsung's curved phone;new Apple iPads?)
The source told Bloomberg that the handsets were still in development and that the plans were not yet completed. The person said, however, that they would probably be released in the third quarter of next year.
Apple was not immediately available for comment.
image: © Daniel Dudek-Corrigan