"The government wants to fix what it sees as the 'news-lisation' of social media," said one source familiar with the talks.
"News-lisation", or báo hoá, is a term used by the authorities to describe the misleading of users into thinking that social media accounts are authorised news outlets.
Authorities would be able to order social media companies to ban accounts that break those rules, they said.
YouTube has 60 million users in Vietnam and TikTok has 20 million, according to 2021 government estimates, although Twitter remains a relatively small player.
Sources told Reuters in April that the new rules, which were originally planned for July, reflected the government's dissatisfaction with social media platforms' take-down rates.