The Institute for Public Policy Research (IPPR) will say, two days before the Leveson Inquiry on press standards is due to issue its report, that old distinctions between media types are "redundant".
It followed uproar last year when media outlets were banned from identifying Ryan Giggs as the footballer who took out a superinjunction over affair allegations, despite almost 30,000 Twitter users naming him.
The Sunday Herald featured Giggs on its front page at the height of the row, but with a strip over his eyes to highlight the worthlessness of the attempts to prevent his name being revealed. He was named inside.
Later this week, the findings of the phone hacking inquiry are expected to suggest greater control of the press.
Labour leader Ed Miliband has called for the recommendations to be implemented as long as they are reasonable.
But freedom of speech campaigners have warned against regulation and have attracted the support of a number of Cabinet ministers including Foreign Secretary William Hague and Education Secretary Michael Gove.
Press regulation is devolved, meaning the Scottish Government will decide on any new regime in Scotland. Last night, Scottish LibDem leader Willie Rennie called on the Scottish Government to say whether it will make a statement to Holyrood when the report is out.
The IPPR argues all media platforms have to be included in a new system. Nigel Warner, author of the report, said: "A new regulatory framework is needed to take a more consistent approach to both upholding standards and sustaining plurality in Britain's media."
A Scottish Government spokesman said: "We are awaiting the recommendations of the Leveson Inquiry, and will respond in due course."