Early production of the new screens has begun at three suppliers: Korea's LG Display Co Ltd, Sharp Corp and Japan Display Inc, a Japanese government-brokered merger combining the screen production of three companies.
It is likely all three of the screen suppliers will get production orders from Apple, which could begin as soon as June. That would allow the new iPhone to go into production as soon as August, if the company follows its own precedent in moving from orders for prototypes for key components to launch.
Apple's decision to equip the next iPhone with a larger screen represents part of a competitive response to Samsung Electronics Co Ltd.
Samsung unveiled its top-of-the line Galaxy smartphone with a 4.8-inch touch-screen and a faster processor earlier this month.
With consumers becoming more and more comfortable using smartphones for tasks they once performed on laptops, like watching video, other smartphone manufacturers have also moved toward bigger displays.
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The latest iPhone 4S was introduced in October of last year and essentially has the same form factor as the iPhone 4, launched in 2010.
Samsung, which this year became the world's largest cell phone maker, sold 45 million smartphones in the first quarter, and sales of the Galaxy phones outstripped the iPhone.
Apple was not immediately available to comment.
Apple's move toward a larger display for the next generation iPhone was earlier reported by the Wall Street Journal.
In addition to being Apple's rival, Samsung is also a major components supplier to the U.S. computer, tablet and phone manufacturer.
The share of the production of new screens that go to each of the three manufacturers working with Apple has not been determined, one source said.
Sales of the touch-screen iPhone now account for about one-half of Apple's total sales, and the phone has been a key source of growth for the company in Asia.
A report in March by a South Korea business newspaper said Apple would use a "retina" display on the next iPhone, the same technology in its latest iPad that enhance image quality.