Vietnam had been one of the top potential beneficiaries of the Trans Pacific Partnership free trade agreement cancelled by Trump, but it has also been building links to the United States amid a maritime dispute with China.
"Prime Minister Nguyen Xuan Phuc affirmed he is ready to visit U.S to promote Vietnam-U.S. tie," the Vietnamese government said on its official Facebook page on Friday.
Phuc also expressed his wish that the United States continues to be Vietnam's leading trade partner.
The former prime minister Nguyen Tan Dung visited the United States in February 2016 to attend a U.S.-ASEAN summit, but the last official state visit was in 2008.
In a telephone call shortly after his election last year, Trump told Phuc he wanted to further strengthen fast-warming ties between the two countries.
Vietnam advanced ties with the United States to a new level under former U.S. President Barack Obama, keen on the United States maintaining its security presence in Asia in the face of territorial claims by neighbouring China.
China claims most of the East Vietnam Sea, while Taiwan, Malaysia, Vietnam, the Philippines and Brunei claim parts of the sea that commands strategic sea lanes and has rich fishing grounds along with oil and gas deposits.
Washington lifted a U.S. lethal arms embargo on Vietnam last May, allowing closer defence links and some joint military exercises.