Journalists are among 10,000 individuals who could face legal action over Twitter messages which wrongly linked Lord McAlpine to the 2 November Newsnight report about child abuse at a North Wales care home.
Legal action is also planned against The Bureau of Investigative Journalism, whose former editor and current lead reporter Angus Stickler were involved in the production of the Newsnight broadcast.
McAlpine has already settled with the BBC for £185,000 in damages plus costs. This is believed to be around the maximum payout he would have achieved had the matter gone to trial.
According to The Daily Telegraph, McAlpine's lawyers are going to seek an even bigger settlement from ITV after This Morning presenter Phillip Schofield handed Prime Minister David Cameron a list of individuals named on the internet as paedophiles which was briefly visible on camera.
His lawyers have now appealed for those who libelled him on Twitter to come forward and appologise for what they have done. Press Gazette understands that those whose Twitter messages showed malice will face the toughest action.
It emerged at the weekend that comedian Alan Davies is among those who could face legal action. He tweeted to his 440,000 followers: "Any clues as to who this Tory paedophile is...?" He then retweeted a response naming Lord McAlpine.
According to The Sunday Times, so far 40 individuals have approached Lord McAlpine's lawyers to apologise. The paper says that each will be asked to pay a nominal amount to charity.
The paper reports that a reporter for Al Jazeera, a freelance writer for The Guardian and the managing director of a PR firm are among those facing possible legal action. Guardian writer George Monbiot and Sally Bercow are among those already potentially in the frame.