Likhachev, who was part of Putin's entourage during his visit to Vietnam last week, said that he had made the offer to Vietnam Prime Minister Pham Minh Chinh.
"We offered all possible options for co-operation... in my conversation with the prime minister of Vietnam," RIA cited Likhachev as saying.
"Rosatom offers foreign partners not only high-power, but also low-power nuclear power plants, both in land-based and floating versions."
Vietnam has no nuclear power plants and scrapped plans to build its first two nuclear power plants in 2016 following the Fukushima disaster in Japan and due to budget constraints.
Before Vietnam cancelled its plans to build the plants, Rosatom had offered Hanoi a project based on high-power units with advanced Russian reactors, Likhachev said.
During the visit, where Putin received a 21-gun salute at a military ceremony, Russia and Vietnam signed agreements on issues including energy, underlining Moscow's pivot to Asia after the West imposed sanctions on Moscow over the conflict in Ukraine.