He accepted £185,000 plus costs from the BBC last week over a Newsnight report, but the spokesman told the newspaper that ITV will have to pay more after This Morning host Phillip Schofield handed the Prime Minister a list of alleged abusers live on air.
The peer reportedly restricted the demand for compensation from the BBC because he was conscious that licence-payers’ money was involved, but the same does not apply to his action against ITV.
The spokesman said: “This was also done in broad daylight in a premeditated way in front of the Prime Minister.
"It was that programme that prompted Lord McAlpine to come out with his statement."
The Times reported that the broadcaster has been given until this afternoon to respond to a demand to pay damages.
Lord McAlpine will receive a payment of £185,000 after a settlement was reached with the BBC over false claims made in a Newsnight report.
George Entwistle will receive a 12-month salary after stepping down from the BBC, he is also reported to be entitled to his full pension.
BBC director general George Entwistle has fallen on his sword following the Newsnight child abuse scandal.