Lord McAlpine was on Monday night close to reaching a six-figure settlement with ITV over Phillip Schofield's onscreen blunder that linked several Conservative politicians with allegations of child sex abuse.

Solicitors for the former Tory party treasurer met lawyers for the broadcaster in London at 4pm to negotiate the terms of the libel payout, expected to be significantly more than the BBC's £185,000 bill.

There was speculation that the final payout could be as much as £500,000 – but ITV would not discuss any figures under negotiation. The broadcaster made contact with McAlpine's lawyers on Monday afternoon, having received a legal letter on Friday.

McAlpine launched legal action against ITV after This Morning host Philip Schofield brandished a list of Tory politicians allegedly linked to child sex abuse, handing it over to David Cameron, whom he was interviewing at the time.

Both ITV and Schofield have apologised for the incident, but McAlpine vowed to sue as he said that the onscreen ambush of the prime minister prompted thousands of libellous Twitter messages.

Lawyers for McAlpine confirmed on Monday that they would seek a quick settlement with ITV, and that they would pursue a larger sum of damages than paid out by the BBC last week as it is a commercial broadcaster rather than a publicly funded one.

Andrew Reid, the solicitor for McAlpine, said last week: "Phillip Schofield managed to embarrass the prime minister as a side part and then destroy my client's reputation," he told BBC Radio 4.

"What he did was very, very low and I am amazed it was allowed. It sent everyone on to the internet – those who couldn't read what was there – to see who being referred to. At the top of the list was Lord McAlpine."

McAlpine is also pursuing libel action against people who used Twitter to repeat the defamatory claim. Lawyers for the Tory peer are believed to have compiled thousands of tweets that name McAlpine and have urged those behind them to come forward to agree a swift settlement.

The media regulator Ofcom began its investigation into ITV over the Schofield incident last week. Schofield and four members of This Morning production staff were reprimanded by ITV last week following an internal inquiry.

Peter Fincham, ITV's director of television, said last week: "I've spoken to Phillip Schofield myself. He realises his mistake. He apologised for it extremely fully and extremely quickly and I discussed that with him and I think he's under no illusions that this was a lapse in ITV journalism; this is something we shouldn't have done.

"I'm not happy that this happened. We have editorial processes and checks in place and, to be honest with you, they weren't followed, so I'm not happy about that."