Lawyers for the Tory peer said they were taking legal action as a result of the programme, which led to the resignation of BBC director-general George Entwistle on Saturday.
In an interview being broadcast today, he said the BBC could have saved “a lot of agonising and money” by simply calling him before the programme went out.
Ofcom said today it was investigating the broadcast, which has fuelled a crisis at the corporation and a revamp of the “chain of command” which had been operating in BBC news since the Jimmy Savile scandal broke.
And the regulator is also investigating ITV1’s This Morning after presenter Phillip Schofield brandished a list of names of alleged abusers he had found on the internet and handed it to the Prime Minister during a live interview, asking if he would investigate them.
The stunt provoked fury last week and ITV said today that disciplinary action had been taken.
Lord McAlpine was mistakenly implicated by Newsnight’s November 2 broadcast in a paedophile ring that targeted children at a care home in Wrexham in North Wales.
Although the programme did not name the peer - referring to only a senior Conservative from the Thatcher era - he was quickly identified online.
Lord McAlpine said the incident had left him devastated and it got into his “soul”.
He told BBC Radio 4’s The World At One programme: “They could have saved themselves a lot of agonising, and money actually, if they had just made that telephone call.
“They should have called me and I would have told them exactly what they learned later on - that it was complete rubbish and that I had only ever been to Wrexham once in my life.”
He added: “It gets into your bones, it makes you angry, and that’s extremely bad for you to be angry, and it gets into your soul, and you just think there is something wrong with the world.”
Lord McAlpine’s solicitor Andrew Reid told Radio 4: “Lord McAlpine is more than aware that the ultimate people who will be paying for any monies that he may receive are, in fact, the licence-payers, the people who really own the BBC, and he is very much aware of this and hence any agreement that is reached is tempered in the light of that.”
Newsnight carried a full, on-air apology for the broadcast a week later. And an official report into the botched investigation by the BBC’s Scotland director Ken MacQuarrie concluded Newsnight staff failed to complete “basic journalistic checks”.
Mr MacQuarrie also found there was confusion about who had the ultimate responsibility for “final editorial sign-off”, adding that the programme’s editorial management structure had been “seriously weakened” as a result of the editor having to step aside over the Savile scandal, and the departure of the deputy editor.
Although legal advice was sought over the report, no right of reply was offered to the unnamed individual at the centre of the allegation.
A BBC spokeswoman said: “The BBC is hopeful that it can agree a settlement with Lord McAlpine today.”
The programme featured an interview with Steve Messham, an abuse victim who said a senior political figure of the time abused him. He later said he wrongly identified his abuser and apologised.
The botched programme heaped more pressure on the BBC, which has been left reeling from the Savile abuse sex scandal.
A review led by former Sky News chief Nick Pollard is already looking into an earlier decision to shelve a Newsnight investigation into the late television presenter’s sexual abuse of youngsters.
BBC director of news Helen Boaden and her deputy Stephen Mitchell have stepped aside from their posts temporarily in the wake of the Savile affair.
The corporation said this was in response to the “lack of clarity” surrounding who is in charge while the Pollard Review is making its inquiries.
The BBC’s head of news gathering Fran Unsworth and Ceri Thomas, editor of the Radio 4 Today programme, are filling in for Ms Boaden and Mr Mitchell until the review is concluded.
Acting director general Tim Davie, who took charge of the BBC following the resignation of Mr Entwistle, vowed on Monday to “get a grip of the situation”.
The corporation has also launched an investigation into the culture and practices at the BBC during Savile’s career and another into the handling of past sexual harassment claims.
Solicitor Mr Reid said those who had named Lord McAlpine on the internet should come forward to settle the matter quickly and avoid further legal issues. He suggested many of them have already been identified.
Speaking in the World At One interview, he said: “What we’re basically saying to people is, look, we know - in inverted commas - who you are, we know exactly the extent of what you’ve done.
“It’s easier to come forward and see us and apologise and arrange to settle with us because, in the long run, this is the cheapest and best way to bring this matter to an end.”
Sally Bercow, wife of House of Commons speaker John Bercow, is among those who alluded to Lord McAlpine on Twitter. She subsequently apologised.