State-run media reported on Sunday that the two sides had "reached agreements in principle," after four days of talks in Washington.
Truong Dinh Tuyen, the Vietnamese trade minister, told Tuoi Tre (Youth) newspaper: "The official signing will be conducted soon, probably in Ho Chi Minh City."
The newspaper quoted Vu Dang Dung, an official at the embassy in Washington, as saying the two countries were expected to officially sign the agreement in early June.
The newspaper did not give details of the agreement which has been in the offing for more than 10 years.
One of issue that dragged the talks on for longer than scheduled was a Vietnamese government's decision to use $4 billion for the garment and textile industry, the newspaper said.
The two sides agreed that Vietnam would scrap this decision upon becoming a WTO member and stop subsidising local garment and textile companies when the two countries sign the agreement, it said.
The US Congress needs to grant Vietnam Permanent Normal Trade Relations, the last step before the country, a communist state, can become a member of the Geneva-based world trade body.
The newspaper said Tuyen, in the capacity as special envoy of Phan Van Khai, the prime minister, has received strong commitments from the US House of Representatives and Senate in giving Vietnam PNTR.
Vietnam has completed deals needed to enter the WTO with all of its other leading trade partners.
It wants to join the world trade body before hosting a summit of the Asia-Pacific Economic Co-operation (APEC) group in Hanoi in November which George Bush, the US president, is expected to attend.
The United States and Vietnam restored diplomatic relations in 1995, 20 years after the end of the Vietnam war.
Since the countries signed a previous business deal in 2001, known as the Bilateral Trade Agreement, Vietnamese exports to the US have grown to more than $6.5 billion in 2005.