Government and Fianna Fáil sources have indicated to RTÉ News that the Taoiseach will make a statement about the controversy surrounding payments he received 13 years ago.
It is uncertain when the statement will be made.
The Minister for Health, Mary Harney, said she believed the Taoiseach would clarify the question of donations he received as Minister for Finance in 1993, which are now being looked at by the Mahon Tribunal.
But in public engagements earlier today, Mr Ahern repeatedly refused to comment on the matter.
Opposition leaders have called for Dáil time to be set aside to discuss the issue when the House sits on Wednesday.
The Green Party said it would make a request for Dáil time in which the Mr Ahern could make a statement.
Speaking on RTÉ Radio’s News At One, Green Party whip Dan Boyle, said his party wanted to question Mr Ahern on the matter.
Mr Boyle said it was not in the Government's interest to allow questions surrounding the donations to remain unanswered.
Labour Party leader Pat Rabbitte said Mr Ahern needed to make a full statement about the matter.
Speaking on RTÉ Radio's Morning Ireland, Mr Rabbitte denied Mr Ahern's claims last week that the Opposition was behind the leaking of confidential information from the tribunal.
He also said he did not believe the tribunal leaked the information, but that it was more probable the leak came from what he described as people being enquired into by the tribunal.