Vinted and eBay could be included in the list of platforms set to be banned for children aged under 16, the culture secretary has said.
Lisa Nandy said the government was "looking seriously" at including the retailing websites in the social media ban "to keep children safe".
The UK's social media ban for under-16s is set to come into force in March next year, with children barred from accessing platforms such as Instagram, TikTok and Snapchat.
In response, eBay said it was looking forward to "understanding more and continuing to work constructively with the government". Vinted said it welcomed "open dialogue" with ministers and the regulator on the issue.
Asked on the BBC's Sunday with Laura Kuenssberg programme whether the government was looking to ban under-16s from Vinted and eBay, Nandy said: "We are looking seriously at doing so in order to keep children safe."
It came after the Sunday Times reported that the UK's social media ban was being expanded to include the popular second-hand online marketplaces.
The move was due to fears that messaging functions on the platforms allowed strangers to groom children, according to the newspaper. It suggested similar reselling platforms, Depop and Facebook Marketplace, would also be included in the list of banned sites.
Businesses and individuals sell a host of goods on eBay, which has been a major global player in the online reselling market for years. The platform states on its website that it currently requires all of its members to be over 18 years old because listings involve "entering into a contract".
Vinted is aimed at over 18s, but its terms and conditions do allow parents or guardians to create accounts for their children, which must be used under parental supervision.
The site, on which users mostly buy and sell unwanted clothes and other fashion items, has grown rapidly recently to reach 17 million UK users.
A Vinted spokesperson said direct messaging was "part of how the platform works" but that it had a "zero tolerance for harmful or explicit content" and had moderation teams and tools to spot and remove "activity that breaks our rules".
"When we identify inappropriate behaviour, we take action, up to a permanent ban or reporting to the relevant authorities," they said.
An eBay spokesperson said the company was "focused on providing a trusted and safe marketplace experience for our millions of customers".
"While the details of the proposed legislation are not yet clear, we look forward to understanding more and continuing to work constructively with the government," they added.
The government announced it would ban under-16s accessing social media in June this year, with children prevented from accessing 10 of the biggest platforms.
YouTube will also be banned for under-16s, but YouTube Kids - a version of the video-sharing app designed to be safe for children - will not be included in the measures.
A complete list of affected platforms has not yet been released, but the government said it would cover those "whose purpose is to enable social interaction and which allow users to post material".
That means platforms that have livestreaming or features that enable the potential for strangers to contact children will also be restricted, which includes gaming sites.
It does not mean that Roblox, the biggest gaming site in the UK for those aged eight to 12, for example, will be banned for under-16s. However, certain features such as its chat function will be restricted.
But Matthew Sinclair, a senior director at the Computer and Communications Industry Association, which represents tech companies, argued that ministers should prevent the rules having "scope creep".
He said a restriction on messaging for under-16s "would not stop at social media and would reach into the services families depend on to stay in touch", and urged the government to "ensure any new restrictions are proportionate and effective."
The UK's ban comes after a similar one was introduced in Australia last year.
Many children there have found ways to get round it, but the UK has said it intends to take a tougher approach.
In recent weeks, attention has turned to how a social media ban would be enforced.
Last month, the communications regulator Ofcom set out its recommendations for the most effective ways to identify which of the UK's millions of social media users are aged over 16.
Rani Govender, head of online child safety at the NSPCC, said the "real question" going forward was how the government ensured age checks were effective.
"But effective age checks are only part of the solution," she added. "Tech companies must also be required to build child safety into every platform, device and AI tool, so children are protected from harmful and illegal content and only able to access age-appropriate services."
