The report, which cited unidentified industry sources, said LG Display will be the sole supplier of organic light-emitting diode (OLED) screens for the Apple watches that go on sale in April.
Samsung Display will also become a supplier for the next version of the smartwatch that is expected to go on sale either sometime in the second half of this year or early 2016, the report said.
LG Display and Samsung Display declined to comment on the report. Apple could not be immediately reached for comment.
Apple has scheduled a special event on March 9, where it is expected to showcase Apple Watch. The watch, which will let consumers check their email, pay for goods at retail stores and monitor personal health information, represents Apple's first major new product introduction since the 2010 launch of the iPad.

Japan Display Inc is also considering building a new plant to supply smartphone screens for Apple Inc, which may shoulder much of the 200 billion yen ($1.68 billion) investment.

The company declined to confirm the report but said it was constantly pursuing opportunities to strengthen its competitiveness, including building a new plant.
"No formal decision has been made regarding any matter that we need to disclose," it added in a statement.