Mr Johnson said he would be going to the Home Office to review papers on the case dating from his time as Home Secretary before offering his advice on the issue to his Tory successor Theresa May.
Fresh questions have been raised about the interception of private voicemail messages of prominent people – which led to the jailing of a News of the World reporter and a private investigator in 2007 – following a report this week in the New York Times.
The report included claims that the newspaper's then editor Andy Coulson, now a senior adviser to Prime Minister David Cameron, was aware that the illegal practice was being undertaken by journalists on his staff – something Mr Coulson has always denied.
It also raised questions about how vigorously the Metropolitan Police had pursued the case.
Mr Johnson, who served as Home Secretary from 2009 to this year, said that during his time in office he had felt "uncomfortable" at the progress being made by the police investigation into the phone-tapping allegations, and had considered calling in HM Inspector of Constabulary (HMIC) to take over the case.
It was now time for Ms May to consider whether this step should be taken, he said.
In a statement, Mr Johnson said: "As Home Secretary I was concerned to ensure the Metropolitan Police conducted a rigorous and thorough investigation into all of the facts and allegations relating to the News of the World phone-tapping case.
"The allegations were extremely serious and involved people from many walks of public life, including democratically-elected politicians.
"Because I felt uncomfortable with the progress being made in the investigation, I considered calling in Her Majesty's Inspectorate of Constabulary to take over the investigation.
"However, following reassuring conversations with senior officers in Scotland Yard I decided not to.
"In the light of the further serious allegations that have surfaced recently, there may now be a case for the Home Secretary to ask the HMIC to investigate.
"It is therefore my intention to go back to the Home Office to review the files relating to the phone-tapping allegations.
"I will then give whatever help I can to the current Home Secretary to ensure she has a complete picture of all the facts."
In a detailed response to the New York Times article, the News of the World said that the American paper's report "failed to provide any new evidence sufficient to support what amount to very serious allegations".
The News International publication confirmed that a reporter had been suspended from duty while an investigation was being carried out into "a serious allegation" about conduct.
But it added: "We reject absolutely any suggestion or assertion that the activities of Clive Goodman and Glenn Mulcaire, at the time of their arrest, were part of a 'culture' of wrong-doing at the News of the World and were specifically sanctioned or accepted at a senior level in the newspaper.
PRESCOTT PREPARED TO TAKE LEGAL ACTION
"We equally reject absolutely any suggestion or assertion that there has continued to be such a culture at the newspaper."
Last year, the Met chose not to launch an investigation into claims that a series of public figures had been the victims of eavesdropping.
Royal correspondent Clive Goodman and private investigator Glenn Mulcaire were the only people to be prosecuted in relation to phone-tapping, and theNews of World has always insisted that theirs was an isolated case.
Former Deputy Prime Minister Lord Prescott said he was prepared to take legal action to force the police to inform him whether his phone was one of those allegedly hacked into.
Lord Prescott said he had demanded the truth about the claims from police and was expecting a reply by September 11.
"If they fail to give us that information, which is clearly available but has to be given to us, I will seek a judicial review," he said.
"The only way the truth can come out is really to have it properly investigated and really have a judicial review. I think it demands at least that."