Rahman will visit Malaysia on Sunday before travelling to China the following day, Dhaka's state-run BSS news agency reported, citing foreign ministry officials.
In Beijing, trade and infrastructure projects will be on the agenda, according to the officials.
Those could include Chinese support for the long-delayed Teesta project, a plan to restore and manage a key Bangladesh river through dredging, embankment construction and irrigation.
"The visits are being viewed as a major diplomatic initiative aimed at strengthening Bangladesh's economic partnerships," BSS reported, citing the foreign ministry.
Malaysia has an estimated 800,000 Bangladeshi workers, more than a third of its foreign workforce.
Bangladesh is largely encircled by land by India, but relations have been strained since a 2024 uprising toppled the government of then-prime minister Sheikh Hasina, an ally of New Delhi.
Ties improved after Rahman won elections and took over in February from the interim administration that had led the country of 170 million people since Hasina's ouster.
But frictions remain. Hasina has been in hiding in India since fleeing the revolution and Bangladesh has repeatedly sought her extradition.
Relations have also deteriorated along the border, with India sending people it deems illegal migrants across the frontier to Bangladesh.
India has long been wary of neighbouring China's regional clout and the world's two most populous countries compete for influence in South Asia.