The Government will move before the end of the week to appoint a former civil servant to inquire into the appointment of a Waterford-based public relations consultant by the Minister for Transport, Mr Cullen.
Ms Monica Leech, one of Mr Cullen's closest political associates, was appointed shortly after he became minister for environment, heritage and local government in 2002.
He moved to Transport after the Cabinet reshuffle last September.
Ms Leech has received some €300,000 from the Department of the Environment under a contract in which she is paid €800 per day plus 21 per cent VAT. She works three days per week.
After the Taoiseach, Mr Ahern, acknowledged in the Dáil that the controversy over Ms Leech's appointment "will not go away", informed sources suggested last night that the investigation will be set up before the weekend.
In what was her first public comment on the controversy, Ms Leech was quoted by RTÉ News yesterday as saying that the past number of weeks had been "dreadful".
She has chosen not to respond to phone calls from journalists since the controversy began.
Mr Cullen has threatened legal action against the Evening Herald over a story in its first edition about his involvement in a 2003 conference organised by the UN Commission on Sustainable Development.
The story was carried over four pages of the paper's first editions but it did not appear in the final edition.
Mr Cullen's spokesman said: "The Minister has demanded an apology and a retraction from the Evening Herald; the story is completely inaccurate.
"If this is not forthcoming, the Minister will instruct his legal team to issue proceedings in the morning."
A spokeswoman for the Herald characterised as a "developing story" the coverage in the first edition. She said the Department of the Environment provided other information "after going to print". She went on to say that the paper would "continue to report on the story in the days ahead".
A UN spokeswoman said that Ireland participated in the conference as a member of the UN and was represented by observers.
"Minister Cullen participated in interactive high-level discussions and informal sessions," said Ms Renata Sivacolundhu, a spokeswoman at the UN department of public information.
The Government will attempt to stop the flow of negative publicity by initiating an investigation by a senior figure experienced in Civil Service procedure.
Mr Cullen's spokesman said he hoped that the investigation could be concluded speedily and deal with the issues comprehensively.