The investment may total up to $400 million, one of them said.
The plan underscores efforts by technology firms led by U.S. iPhone maker Apple and Taiwanese device assembler Foxconn to lower supply chain exposure to China amid trade and geopolitical tension between Beijing and Washington and production disruption caused by China's Covid-19 containment measures.
BOE is in talks to rent dozens of hectares of land in north Vietnam to add to its relatively small plant in the south that supplies mostly television screens to South Korea's Samsung and LG Electronics Inc, the people said, declining to be identified as negotiations were confidential.
BOE declined to comment.
Northern Vietnam has in recent years attracted significant investment from electronics giants, becoming a major hub for the production of smartphones, computers and cameras, including flagship goods from Apple and Samsung.
Hon Hai Precision Industry Co Ltd (Foxconn) and China's Luxshare Precision Industry also make or plan to assemble a number of Apple products in the area such as laptop and tablet computers.
BOE plans to rent up to 100 hectares and use 20% for a plant making remote control systems at a cost of $150 million, one of the people said.
The rest would be for displays, with BOE spending $250 million to build a plant on 50 hectares while suppliers would use the remaining 30 hectares, all by 2025, the person said.
BOE plans to make the more sophisticated organic light-emitting diodes (OLED) screens at the site rather than liquid-crystal displays (LCDs), the person said.
Apple, which included BOE in its 2021 list of manufacturing partners, uses OLED screens for its latest iPhone smartphones.
China's biggest display maker by output is set to become the largest supplier of displays for new iPhones by 2024, analyst Kuo Ming-chi at TF International Securities forecast last week.
The U.S. tech giant, however, plans to start making mobile screens in-house by next year, Bloomberg reported on Wednesday.
Apple declined to comment.
BOE's Vietnam plan is not specifically aimed at supplying Apple, the person said.
Customer Samsung, the world's largest smartphone maker, produces half of its handsets in Vietnam while LG has a large operation in the country and is planning new investment.