Apple supplier Japan Display alludes to increased iPhone orders ahead of Sept. 9 event

Homma in an interview with Reuters outlined Apple's seemingly insatiable demand for iPhone screens, suggesting the company expects high levels of consumer interest when it announces this year's handset refresh. He added that economic headwinds in China don't appear to be a concern for Apple.

"They're coming to us with more orders, saying 'give us more, give us more.' They keep increasing," Homma said.

The executive's comments come after Apple CEO Tim Cook allayed fears over a wavering Chinese market in a rare email to CNBC's Jim Cramer. Citing daily updates on Apple's Chinese business, Cook said the company experienced "strong growth" through July and August.

"Growth in iPhone activations has actually accelerated over the past few weeks, and we have had the best performance for the App Store in China during the last 2 weeks," Cook said.

With a growing middle class and constantly expanding LTE network infrastructure, China is a key growth market for Apple. As such, the company has ramped up efforts to sell its products in the region. For example, Apple is looking to triple the number of brick-and-mortar Apple Stores in China by mid-2016.

Apple is widely expected to announce a next-generation iPhone lineup at a special event on Sept. 9, which could also see the debut of a new Apple TV.