That second size would create a phablet-sized iPhone. The first size, 4.7-inches, is been seen frequently with the typical high-end Android and Windows Phone smartphone screen sizes running from around 4.3-inches to 5.0-inches, with the window constantly changing.
Those two models, the report said, are planned for release in the second half of next year and would feature displays with that curve downward at the edges, said an anonymous source, who declined to be identified because the details of the project are not public (and won't be until Apple launches the devices).
In addition to the screen size changes, touch sensors on the display that will be able to distinguish between light or heavy pressure on the screen may be incorporated into later models, the same source said.
Plans are to release the new phones in Q3 of 2014, which would match the annual release cycle for the iPhone. This year's iPhone 5s was released on Sept. 20.
While this sort of jives with an earlier report, in September, which said that Apple was testing devices with screens up to six-inches in size, it's a bit early for iPhone 6 (or whatever) rumors to begin.
Quite a few rumors start early, then never come to fruition. As an example, in January of this year, it was rumored that the iPhone 5s would sport a 4.3-inch screen. That, obviously, did not happen, despite being quite a bit close time-wise to the iPhone 5s launch than this rumor is to the iPhone 6 launch.