The new devices are said to boast screens of 4.7 and 5.5 inches in size, a significant increase on the four inch display currently used by the iPhone 5s.
The Bloomberg article, which cites people familiar with the company, also claims a possible iPhone 6 will be "thinner and rounder" than its predecessor and include features such as a curved screen and intricate pressure sensors.
The 4.7 inch iPhone will likely go on sale in September, when Apple traditionally releases its latest mobiles, while the simultaneous launch of the 5.5 inch version remains a possibility.
The demand for smartphones with larger screens is growing as advances in technology allow people to use their phones for more and more of their entertainment needs. According to market research by Forrester, 40 per cent of Android phones sold in China last year had screens of five inches or more.
The iPhone remains a huge driver of profit for Apple and produced $91bn in revenue last year.