The new handset, expected to be called the iPhone 6, is to come in two versions with a 4.7- or 5.5-inch screen, both bigger than the current four-inch panel, the respected Nikkei business daily said, without citing sources.
US-based Apple is ordering its higher-resolution liquid crystal display screens from Japanese electronics giant Sharp, Japan Display and South Korea's LG Display, it added.
Apple released the iPhone 5 in September 2012 and newer versions in the series last year.
A Japan-based spokesman for the California tech giant could not be immediately reached for comment on the Nikkei report, which was widely picked up by a string of technology news websites.
The Nikkei story comes after Taiwan's Commercial Times said this month that Taiwan Semiconductor Manufacturing Co. had started producing chips for the next iPhone.
That news fed rumours that Apple is reducing its reliance for parts on South Korean giant Samsung, its main competitor in the mobile phone market and a bitter rival with which it is contesting several copyright court battles globally.
Samsung in February unveiled its new flagship Galaxy S5 smartphone armed with a fingerprint scanner and a built-in heart rate sensor, as it tries to cement its leadership of the multibillion-dollar market.
However, the South Korean giant voiced annoyance after domestic telecoms operators released its latest smartphone ahead of schedule in order to dodge sales restrictions imposed by regulators. The world's biggest mobile phone maker had planned a worldwide debut of the Galaxy S5 on April 11.
Samsung made about 30 per cent of all smartphones sold globally last year, nearly twice the share of Apple.
A survey by International Data Corporation (IDC) last month said Google's Android system -- used by Samsung among others -- extended its gains over Apple's iPhone in the last quarter of 2013, and Windows Phone grabbed the number three market position.
But other challengers are moving up the ranks with Taiwan's HTC Corp. having launched an update of its HTC One smartphone while Sony has seen strong sales of its Xperia offering.
Global shipments of smartphones last year topped a billion for the first time, up 38.4 per cent from the 725.3 million shipped in 2012.