The Nikkei, citing sources, said that Apple was "aggressively testing" BOE's flexible organic light-emitting diode (OLED) displays, adding the company would decide by the end of the year whether to take the company on as a supplier of the panels.
The move is aimed at cutting costs and reducing Apple's reliance on Samsung, the Nikkei reported.
The U.S. tech giant is expected to unveil its new flagship phones in September, and speculation has grown over what Apple will bring to the table with the latest models. Last year, the company brought out three new models, the XS, XS Max and XR.
Analysts don't expect the new iPhone, which has been dubbed the iPhone 11 by industry watchers, to include significant updates to previous models. The expectation is that the company will not release phones with any major changes, including 5G, until 2020.
Selecting a Chinese company would be a surprising move, given the company has warned of the impact of the U.S.-China trade war on its business. Many of Apple's major products, including the iPhone, are produced in China.
The firm has reportedly considered moving some production out of the country, but got a slight reprieve earlier this month after the U.S. announced it would delay tariffs on electronics and other consumer products made in China until mid-December.
Apple was not immediately available for comment when contacted by CNBC.
You can read the full Nikkei report about Apple's production move here.