Friends stressed that he had not been contacted by police, but a spokesman for the former News of the World editor said he would be prepared to co-operate with Scotland Yard following claims by ex-NoW journalist Sean Hoare.
A spokesman for Mr Coulson said: "Andy Coulson has today told the Metropolitan Police that he is happy to voluntarily meet with them following allegations made by Sean Hoare.
"Mr Coulson emphatically denies these allegations. He has, however, offered to talk to officers if the need arises and would welcome the opportunity to give his view on Mr Hoare's claims."
Mr Hoare has claimed Mr Coulson knew of eavesdropping tactics used at the newspaper during his time in charge, something he has consistently denied.
Metropolitan Police Assistant Commissioner John Yates said today that he would be prepared to investigate Mr Hoare's allegations, which first surfaced in the New York Times.
Mr Coulson came under renewed pressure last week after former journalists told the US paper that the practice of phone hacking was far more extensive than the News of the World acknowledged at the time.
Labour MPs and ex-deputy prime minister Lord Prescott have called for a fresh inquiry, and Lord Prescott is also seeking clarification from the Met over whether his phone was tapped.
Mr Yates told the BBC Radio 4 Today programme: "We have always said that if any new material, new evidence, was produced we would consider it."
Of Mr Hoare's allegation, Mr Yates said: "It is new and we will consider it and be consulting with the Crown Prosecution Service before we do.
"This is the first time we have heard of Mr Hoare or anything he has to say. We focused our resources where we thought we could get the best evidence.
"He has come from nowhere. We are surprised that the New York Times did not alert us to this information earlier than they did.
"We have to focus our investigation where we can get the best evidence, not go on a wild goose chase."
He refused to speculate on how many people's phones may have been hacked but stressed : "All I would say is we take our obligations regarding telling victims very seriously.
"There's a misunderstanding here that suggests just because your name features in a private investigator's files, your phone has been hacked.
"The fact that John Prescott's name appears on an invoice does not mean his phone has been hacked. It means he is of interest to a private investigator. That's what private investigators do.
"I believe there is no evidence that his phone has been hacked. I have made that very clear on a number of occasions."
Asked if the original probe had been mishandled, Mr Yates said: "No. I absolutely don't accept that. This was a very, very thorough inquiry. It resulted in the conviction of two people, it resulted in a very complex area of law being clarified and it sent an extremely strong deterrent to other people."
The NoW's former royal editor, Clive Goodman, and a private investigator used by the newspaper were jailed in 2007 following phone hacking revelations.
Mr Coulson said at the time that he had not known of the practice but resigned his editorship, before joining then Tory leader David Cameron as communications boss, moving with him into No 10.
In a statement released today, the News of the World accused the New York Times of being motivated by commercial rivalry.
It said: "The News of the World repeatedly asked the New York Times to provide evidence to support their allegations and they were unable to do so.
"Indeed, the story they published contained no new credible evidence and relied heavily on anonymous sources, contrary to the paper's own editorial guidelines.
"In so doing, they have undermined their own reputation and confirmed our suspicion their story was motivated by commercial rivalry.
"We reject absolutely any suggestion there was a widespread culture of wrongdoing at the News of the World."
Friends of Mr Coulson were keen to stress today that his statement was not prompted by a police approach, and pointed out that a new investigation had not yet even been launched by Scotland Yard.
The Prime Minister's spokesman said today that Mr Cameron was "completely happy with the job Mr Coulson is doing".
The spokesman added: "The reports that have been in the media over the weekend do not change the situation for the Prime Minister. Andy Coulson has been clear in denying the allegations that have been made.
"Clearly, if the police want to look at this, then that is a matter for them and we would not want to interfere."
Mr Yates is bound to be quizzed about the phone-hacking affair when he appears before MPs at the Commons Home Affairs Select Committee tomorrow afternoon, in his role as the yard's Assistant Commissioner for Specialist Operations.
He is due to answer questions about "topical aspects of his role".
There will also be pressure from Labour MPs for the Government to make a Commons statement on the issue this afternoon, on their first day back at Westminster after the summer break.
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