Taoiseach Bertie Ahern has confirmed that he will announce "shortly" a successor to the Minister of State for Education and Science, Síle de Valera, who stepped down from her post yesterday.
Mr Ahern said he hadn't given the matter much thought coming up to the Budget but that he now intended to address the issue.
He will bring a nomination to Cabinet on Tuesday and will make the announcement afterwards.
The Taoiseach said there is a short period left in the life of the Government and there are a few people who would "like to be set up", but he only had one post to give.
"I have to pick one of a small few. A number of people have been around and their names are common to everyone.
"I just have to pick one of these. I would love to be able to pick three of them, but I can't."
The firm favourite for the job is Dublin North Central TD Seán Haughey, who was deeply disappointed when he was passed over for a junior ministry last February after the resignation of Ivor Callely.
He said in a radio interview at the time he was considering his future in politics, but he later met the Taoiseach and said the outcome was "satisfactory".
Other potential Fianna Fáil backbenchers being speculated on are Tipperary North TD Maire Hoctor; Donegal North East TD Cecilia Keaveney; and Cork South West TD Denis O'Donovan.
Ms de Valera (52) is the granddaughter of the former taoiseach, president and Fianna Fáil founder, Eamon de Valera.
She is a niece of former TD Vivion de Valera and a first cousin of the current Minister for Community, Rural and Gaeltacht Affairs, Eamon Ó Cuív.
She announced in November 2005 that she would not be contesting the next general election and to much surprise it was announced she was to stay in her junior ministerial post for a year.
The Clare TD, who intends to pursue a PhD in psychology, finished her last day in the Department of Education yesterday where she had special responsibility for adult education, youth affairs and educational disadvantage, a post she held since 2002 when she was dropped from the Cabinet.
Last night the Minister for Education, Mary Hanafin, paid tribute to Ms de Valera and wished the best with her studies.
Mr Ó Cuív told The Irish Timesthat he wished Ms de Valera well and said he will be sad to see the de Valera name leave the Dáil next year.