Tillerson has so far kept a low profile and it will be his first visit to the region since he became President Donald Trump's top diplomat last month.
The former oil executive is expected to visit Japan on March 17 and 18 on the first leg of his Asian tour and hold talks with his Japanese counterpart Fumio Kishida as well as Prime Minister Shinzo Abe, the Nikkei business daily said.
During the Beijing leg of the Asia trip, Tillerson plans to meet with Chinese Foreign Minister Wang Yi and possibly also with President Xi Jinping, Kyodo News said, quoting unnamed diplomatic sources.
The two major powers are expected to arrange a meeting between Xi and Trump in the United States as early as April, they said.
Tillerson first met with counterpart Yi at a G20 meeting in Germany last month, and urged Beijing to help rein in North Korea.
Trump however later reaffirmed the position in a conciliatory phone call to Xi.
Several of Trump's cabinet, including Tillerson, have also warned Beijing against throwing its weight about in the South China Sea, insisting the US would intervene if necessary to preserve international rights of navigation.
However, China shares US concerns about Pyongyang's nuclear weapons -- though it prefers negotiations to new sanctions, which it fears could destabilise North Korea.
In Seoul, Tillerson plans to hold talks with South Korean Foreign Minister Yun Byung Se at which North Korea's weapons development as well as the February murder of the half-brother of North Korean leader Kim Jong-Un in Malaysia are likely to be discussed, Kyodo said.
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