The trio also includes an upgraded handset the same size as the current iPhone X and a less expensive model with some of the flagship phone's key features.
The iPhone maker is already running production tests with suppliers and is expected to announce the new phones this fall. However, the plans could still change, the report said.
Apple did not immediately respond to a request for comment.
The Cupertino-based company earlier this month forecast disappointing revenue of US$60 billion to US$62 billion for its fiscal second quarter ending in March, with a number of media reports pointing to slack demand for iPhone X after unit sales failed to meet expectations in the run-up to Christmas.
With the global smartphone market set to stay flat or even shrink after meagre growth of one percent last year, vendors are focusing on features designed to encourage consumers to ditch their old phones earlier than they would have previously.
Samsung on Sunday unveiled its flagship Galaxy S9 smartphone with an emphasis on visual applications for social media, hoping to attract tech savvy young consumers to weather a market slowdown.
DJ Koh, Samsung's president of IT and mobile communications, said the most important function of a phone today was "visual communication", and the Galaxy S9 had been designed for the visual and social generation.
It features improved cameras, an artificial intelligence-powered voice tool, and social media functions that are easier to deploy than previous offerings.
Bloomberg said the giant iPhone, resembling a phablet, will have a close to 6.5-inch display. While the body of the phone will be about the same size as the iPhone 8 Plus, the screen will be about an inch larger thanks to the edge-to-edge design.
The phablet is code named D33, the agency said, citing a person familiar with its development.
Apple is also preparing an update to the regular-sized iPhone X that is internally dubbed D32, people familiar with the product said.
The people said both these phones are expected to use next-generation A12 processors and will continue to include stainless steel edges and will be Apple's high-end smartphone offerings.
(Reporting by Sonam Rai in Bengaluru; Editing by Saumyadeb Chakrabarty)