The ex-Conservative Party treasurer and life peer issued a full statement on the matter while reserving the right to sue those who had defamed him.
Former Bryn Estyn resident Steve Messham had claimed on BBC's Newsnight that he had been abused at the home by an unnamed man who was a senior politician while Margaret Thatcher was prime minister.
McAlpine noted that his name and the allegations had been linked in the public domain and said that "in order to mitigate, if only to some small extent, the damage to my reputation I must publicly tackle these slurs and set the record straight".
The peer expressed "every sympathy for Mr Messham and for the many other young people who were sexually abused", describing their abuse of vulnerable children as "particularly abhorrent".
McAlpine concluded: "I wish to make it clear that I do not suggest that Mr Messham is malicious in making the allegations of sexual abuse about me. He is referring to a terrible period of his life in the 1970s or 1980s and what happened to him will have affected him ever since.
"If he does think I am the man who abused him all those years ago I can only suggest that he is mistaken and that he has identified the wrong person.
"I conclude by reminding those who have defamed me or who intend to do so that in making this statement I am by no means giving up my right to seek redress at law and repeat that I expressly reserve my rights to take all such steps as I and my solicitors consider necessary to protect my interests."
Messham has since said that a case of mistaken identity had led to McAlpine being linked to the claims, and offered his "sincere and humble apologies to him and his family".
"After seeing a picture in the past hour of the individual concerned, this [is] not the person I identified by photograph presented to me by the police in the early 1990s, who told me the man in the photograph was Lord McAlpine," he said in a statement.