The government announced in June this year that it would ban under-16s from accessing social media, with children to be prevented from using 10 of the biggest platforms. YouTube will be banned for under-16s. YouTube Kids, a version of the video-sharing app designed to be safe for children, will not be included.
Last month, the communications regulator Ofcom set out its recommendations on the most effective ways to identify which of the UK's millions of social media users are aged over 16.
She confirmed reports that the two marketplaces could be added to the list of platforms set to be restricted next March.
Services that offer livestreaming, or features that could let strangers contact children, will also be restricted. That category includes some gaming sites.
Vinted has not responded to requests for comment.
Vinted mostly sees users buy and sell unwanted clothes and other fashion items. The site has grown rapidly in recent times and now has 17 million UK users.
The rule does not mean that Roblox, the biggest gaming site in the UK for eight- to 12-year-olds, will be banned for under-16s.
Vinted states on its website that it requires all members to be over 18 because listings involve"entering into a contract". It also says users need to be at least 18 years old. Ministers have not yet published a complete list of affected services. The government said the ban would cover platforms"whose purpose is to enable social interaction and which allow users to post material".