Lawyers for Lord McAlpine are seeking a larger payout from ITV than the £185,000 they received from the BBC last week, they have confirmed.
The former Tory politician's legal team said they are looking to get a larger figure from ITV's This Morning, which is thought to have until this afternoon to respond to demands.
The broadcaster sparked fury after presenter Phillip Schofield brandished a list of names of alleged abusers which he had found on the internet and handed it to the Prime Minister during a live interview, asking if he would investigate them.
Ofcom has also launched an investigation into the incident, while ITV said that disciplinary action had been taken.
The broadcaster has been contacted by Lord McAlpine's lawyers, and is expected to have to respond by the end of today.
An ITV spokesman said: "We have received correspondence from Lord McAlpine's representatives and we will be responding in due course."
ITV is the second name in a long list of organisations and individuals who wrongly linked Lord McAlpine to a paedophile ring. Action is also being prepared against a large number of Twitter users - including the wife of the Commons Speaker - who identified the peer in connection with the false sex abuse claims.
Lawyers for the peer reached a £185,000 settlement with the BBC last week after it broadcast a botched Newsnight investigation into child abuse at a North Wales care home.
Lord McAlpine was mistakenly implicated by Newsnight's November 2 broadcast in a paedophile ring that targeted children at the care home in Wrexham. Although the programme did not name the peer - referring only to a senior Conservative from the Thatcher era - he was quickly identified online.
Lord McAlpine has previously said he was "delighted" to have reached a quick and early settlement with the BBC. "I have been conscious that any settlement will be paid by the licence fee-payers, and have taken that into account in reaching agreement with the BBC," he said last week.