The Guardian alleges that thousands of high profile figures - including ex-deputy PM John Prescott - had their mobile phones hacked in to by the paper that Coulson edited until January 2007.
Prescott and former home secretary Charles Clarke have already called for Coulson to be sacked.
Conservative leader David Cameron this morning insisted Coulson's job is safe, but Labour sources said the party will continue to target the former tabloid editor up to the general election.
One senior Labour source in regular contact with Gordon Brown's inner circle told PRWeek: ‘Cameron wants to present himself as the man who's going to clean up politics. That's going to be difficult if the public think his right-hand man is a complete sleazeball.'
Another Labour insider said that senior party figures had been thrashing out a strategy to target Coulson since the news emerged yesterday. The source said the aim was have Coulson ‘wounded, but still there'.
The source added that if Coulson was to hang on by Cameron's side, then Labour would be able to target him heavily him during last four weeks of a general election campaign.
And former Downing Street comms director Alastair Campbell said on his blog this morning that the Guardian's story raised questions for Cameron, adding: ‘Those questions have not gone away. They are only just beginning.'
PM Gordon Brown is believed to be especially keen to target Coulson, who he blames personally for a number of Tory attacks on his character, including branding the PM a ‘ditherer'.
Coulson took the job of Conservative Party communications director in July 2007. In a statement last night, Coulson focused on one element on the Guardian's exclusive: ‘This story relates to an alleged payment made after I left the News of the World two and a half years ago. I have no knowledge whatsoever of any settlement with Gordon Taylor.'
Gordon Taylor, the chief executive of the Professional Footballers' Association, received a £700,000 payment from News Group, The Guardian reports today.
Speaking outside his home in west London this morning, Cameron said: ‘It's wrong for newspapers to breach people's privacy with no justification. That is why Andy Coulson resigned as editor of the News of the World two-and-a-half years ago.
'Of course I knew about that resignation before offering him the job. But I believe in giving people a second chance. As director of communications he does an excellent job for the Conservatives, in a proper, upright way at all times.'