The Standards in Public Office Commission (SIPOC) is to decide this week if it will open a full investigation into contracts given to a supporter of the Minister for Transport, Mr Cullen.
The independent body, which is headed by Mr Justice Matthew P. Smith, is currently inspecting files from the Department of the Environment and the Office of Public Works.
A decision by the commission to begin an inquiry would prompt calls for Mr Cullen to stand down from the Cabinet, in line with the example set by Fianna Fáil TD Mr Ned O'Keeffe when he faced an investigation during his time as a minister of state.
Last night sources close to the commission said it was "impossible to speculate" on the final decision of the body.
The meeting is most likely to be on Wednesday or Thursday.
An investigation into the affair by former top civil servant Mr Dermot Quigley found that Mr Cullen had not broken any rules in the appointment of supporter Ms Monica Leech as a PR consultant. However his actions had created "a perception of impropriety".
Asked last night if Mr Cullen would stand down in the face of a full inquiry by SIPOC, his spokesperson said: "Let's see what the commission does. To say anything now would be premature."
Calling for a SIPOC investigation, the Labour Party said Ms Leech's contract with the Office of Public Works during Mr Cullen's time there was constructed to avoid rules set down by the Ethics in Public Office Act.
"There are strong grounds for the Standards in Public Office Commission establishing a formal inquiry into this affair," said Labour TD Ms Joan Burton.
"Someone at the OPW was very much aware of the requirements of the ethics Act in relation to special advisers, and that Mrs Leech's appointment to the OPW was designed to escape most - but not all - of those requirements."
For example, each special adviser to a minister must draw up a statement of interests and lodge it with the Houses of the Oireachtas if he/she is paid more than the maximum salary (standard scale) of a higher executive officer in the Civil Service.
"Payment under Ms Leech's OPW contract was one grade below that - equivalent to executive officer standard rate salary scale at the time, to which specific reference was made in the papers," she said.
Demanding a review of all State PR contracts by the comptroller and auditor general, the leader of Fine Gael, Mr Enda Kenny, criticised Mr Cullen.
"While the Quigley report exonerates him in the Taoiseach's view he has obviously strayed very close to the line," Mr Kenny told RTÉ's This Week programme. "It appeared to me that he chose the least experienced and more expensive. If that is the case there is something wrong with the process."
The leader of the Green Party, Mr Trevor Sargent, also called for a full inquiry.
"The Quigley report is being held up by Taoiseach Bertie Ahern as showing that the conduct of Minister Cullen has been free of any impropriety or wrongdoing. Bertie Ahern's casual interpretation of the report as having exonerated the actions of Minister Cullen says much about the Taoiseach's perception of what constitutes impropriety."