Ministers will legislate for a new "duty of care" to be policed by an independent regulator, according to the proposals leaked to the Guardian, the Press Association reported.
The watchdog will have powers to impose substantial fines for breaches by companies and hold executives personally liable, the newspaper reported.
The plans are expected to be published in a long-awaited Government White Paper on online harm next week.
"We will shortly publish a White Paper which will set out the responsibilities of online platforms, how these responsibilities should be met and what would happen if they are not," a government spokesman said. "We have heard calls for an internet regulator and to place a statutory 'duty of care' on platforms, and have seriously considered all options."
It comes amid mounting pressure on social media companies to reform and accept new regulation following high-profile criticism of the industry.
A wide range of reports and experts have called for tighter rules, while the case of teenager Molly Russell highlighted the danger of harmful content online.
She was found to have viewed content linked to self-harm and suicide on Instagram before taking her own life in 2017.
Her father, Ian Russell, has added his voice to others suggesting the time of social media self-regulation has passed.
"Up until now they have chosen their own course. Governments have allowed social media platforms to be self-regulated, but remember this really is a matter of life and death and it's getting worse," he said last month. "Now is the time for the UK Government to bring effective internet regulation, with strong sanctions as backup.
"Now is the time for the UK to lead the world in making the online world a safer place, especially for the young."