Taoiseach Enda Kenny is likely to wait until after the month's mind mass for the late junior minister Shane McEntee before naming his replacement, senior government sources have said.
Mr Kenny, who delivered an emotional graveside oration at Mr McEntee's funeral, is not "in any rush" to name a successor and is keen to pay due respect to the memory of his late friend.
His spokesman had a firm "no comment" on the matter this weekend, but well-placed sources have said Mr Kenny had not even yet had discussions with key advisors about naming a replacement.
Mr McEntee, who took his own life on December 21, was a father of four and had represented the Meath East constituency since 2005, when he filled the seat vacated by former Taoiseach John Bruton.
Despite the Taoiseach's desire to wait, speculation is mounting as to who will be promoted to fill the vacant position at the Department of Agriculture.
On geographical grounds, given that he represents the neighbouring Meath West constituency to Mr McEntee, Mr English is seen as a frontrunner.
Elected as the youngest TD in 2002, Mr English was made secretary to the Fine Gael parliamentary party. He was also a junior justice spokesman in the 30th Dail.
Despite opposing Mr Kenny in the heave, he has since done his best to be a model team player, regularly going out to bat for the Coalition in trying circumstances.
However, much has been made of Andrew Doyle's candidacy in recent days, with many pointing to his farming background as making him a perfect fit for the post.
Mr Doyle, who also opposed Mr Kenny in the 2010 heave, has attracted some decent press in the past 12 months as chairman of the Communications, Natural Resources and Agriculture Committee during the hearings into the Fr Kevin Reynolds RTE debacle.
Ms Doherty, who represents the same Meath East constituency as the late Mr McEntee, has distinguished herself during her first term as a TD. But there is no doubt that such a reward for a newcomer would upset some of her longer-serving colleagues.
Notwithstanding her talents, Mr Kenny's style would suggest that Ms Doherty has at best an outside chance.
There are several Kenny loyalists who would feel that their time has come for reward. While TDs like Bernard Durkan and Cavan's Joe O'Reilly have been mentioned, according to senior party figures they are unlikely to be chosen.
Cork North West's Michael Creed, who was spokesman on agriculture in the last Dail, considers himself worthy but also finds himself out in the cold. Jerry Buttimer's name has been mentioned as a late runner, given his impressive handling of the Oireachtas Health Committee hearings on abortion last week.
In terms of filling the Meath East seat vacated by Mr McEntee's passing, under new rules the by-election has to take place by June.
Ideally, the party would hope for a member of the McEntee family, with Shane's daughter Helen (who worked as his personal assistant in the Dail) mentioned. However, her youth and the tragedy of her father's death may dissuade her from running.
MEP Mairead McGuinness has also been mentioned as a possible candidate.