Japanese Apple news site Macotakara claims that the technology giants have already shipped batches of the LCD screens, which are expected to be used by the next iPhone.
The news backs up previous speculation that the next generation iPhone will sport the 4-inch display that was rumoured for the iPhone 4S.
It was previously reported that Sharp has been commissioned to build a LCD display using its IGZO technology for the third-generation iPad, which is expected to debut in 2012.
"IGZO technology is perfect in that it offers near-OLED power consumption while having a lower cost and thinness that is only 25% greater than OLED, based on our checks," said Jeffries analyst Peter Misek.
Apple has also allegedly hired an unspecified Taiwanese company to develop screens for a "fundamentally changed" fourth generation iPad, Apple Insider reports.
The rumoured 4-inch display iPhone is said to be in development for 2012.