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It says suppliers of the iPhone's screens are set to ramp production soon in order to hit the September release.
The Nikkei also says the iPhone will come in two screen sizes, 4.7-inch and 5.5-inch.
Right now Apple's iPhone 5 and 5S are 4-inch screens. Apple is the only major phone manufacturer with a screen that small.
The latest flagship Android phones from Samsung and HTC both come with 5-inch screens.
As a result, the iPhone's screen feels small and cramped relative to its Android competition.
In addition to enlarging the screen, Apple will make the resolution on the new iPhones significantly higher, says the Nikkei.
For Apple, this has the potential to be massive. Brian Marshall at ISI said, this would be the "mother lode" of upgrade cycles for Apple. The new iPhones, with big screens, will be significantly different than older models of the iPhone, and as a result Marshall expects big sales to existing customers.