Mr Brown was said to have written at least one letter to the Metropolitan Police over concerns that his mobile phone was being targeted while he was Chancellor of the Exchequer, according to the Independent on Sunday.
The concerns were said to have coincided with the latter stages of Andy Coulson's editorship of the News of the World.
Mr Coulson announced on Friday that he was resigning as David Cameron's director of communications amid continuing allegations of phone hacking by the paper's journalists while he was in charge.
Mr Brown's office declined to comment on suggestions that the former prime minister had raised the matter with the police, but Ms Harman said that it was important that all allegations were properly investigated.
"Hacking into people's phones is illegal. Obviously the criminal law has got to be complied with and if it is broken then it should be investigated by the police and it should be enforced," she told Sky News's Murnaghan programme.
Earlier, Tony Blair's former communications director Alastair Campbell denounced the "lacklustre" way in which the police had investigated the phone hacking allegations as a scandal. "When you compare and contrast the way the police pursued Tony Blair on the so-called cash-for-honours nonsense and the lacklustre way in which they have handled this, then there is a very, very big difference," he told Sky News.
"There must be reasons behind that which will, I think, become part of an unfolding scandal."
Meanwhile, a media lawyer has claimed that the phone-hacking allegations were not just confined to one newspaper.
Mark Lewis, who acted for Gordon Taylor of the Professional Footballers' Association in a damages claim against the News of the World, said he was representing four people who believe they were targeted by other newspapers.
Energy Secretary Chris Huhne said: "It seemed to me clear for a long time that the number of people that were being hacked clearly was not consistent with it being one rogue reporter who happened to be the royal correspondent.
"Why would the royal correspondent be interested in hacking the voicemails of Simon Hughes for example?"
He went on: "It is very clearly important for Sir Paul Stephenson, having now taken control of the Met to make sure that, along with the CPS (Crown Prosecution Service) this is really dealt with."
He told the BBC's Politics Show: "I have worked on a newspaper and I have been a journalist and it does seem to me totally implausible that this was a situation where it was limited to one journalist.
"We now know that one very senior member of the News Of The World executive staff has been suspended.