Lee, speaking at a press event at the airport in Hong Kong as he returned from a trip to Beijing, told reporters that the goal for the reopening will be to return the border to its state before the virus outbreak.
Restrictions on travel across the border between Hong Kong and the mainland were first imposed in early 2020.
The border reopening has been postponed several times due to outbreaks in either Hong Kong or the mainland. Hong Kong and China have trailed most of the world in easing stringent Covid-related rules.
People in the Chinese special administrative region of Hong Kong can currently only access the mainland via the city's airport or two check points: one at Shenzhen Bay and the other via the Hong Kong-Zhuhai-Macau bridge.
Most other border points including the West Kowloon high speed rail terminus have been closed since early 2020.
Local media have reported that preparations were already under way for reopening the border, including deploying thousands of officers from the city's customs, immigration and police services.