Hong Kong's Hang Seng index was up 1.5 percent after a few hours of trading.
Shanghai and Shenzhen's composite index were simultaneously up 0.5 and 0.6 percent, respectively.
The Tokyo Stock Exchange's Nikkei 225 index was up 0.2 percent at lunch local time. The broader Topix index, however, stood at minus 0.1 percent.
The White House's economic adviser Kevin Hassett signaled on Sunday that a call between US President Donald Trump and Chinese President Xi Jinping may be expected this week, which could inject hope that the tense trade relations between the countries may ease somewhat.
China has not commented on the reports, however.
