Two models, said to be in the pipeline for release in the second half of next year, will sport larger displays with glass that curves downward at the edges and sensors that can detect different levels of touch pressure, Bloomberg quoted the source -- who declined to be identified because the details aren't public -- as saying.
Two screen sizes -- 4.7 inches and 5.5 inches -- would put the next iPhone in direct competition with large-screen Android phones such as the 5.7-inch Galaxy Note 3 from Samsung.
"Screen size is one of the things where Apple has to catch up to the Android camp," Dennis Chan, an analyst at Yuanta Financial Holding Co. in Taipei, said.
Other smartphones are already out with curved displays, including Samsung's Galaxy Round and LG's G Flex, although both are available only in South Korea at present.
2014: The Year in Music [PHOTOS]