The appointment will take place today, just hours before Fine Gael’s former coalition partner Labour announces its new list of public spokespeople — including a number of politicians who lost their seats.
Before the first sitting of the Seanad today, Taoiseach Enda Kenny will be tasked with appointing someone to lead the Government party in the upper house.
While no decision had been made last night, a number of high-profile senators — including ex health and children minister Mr Reilly, ex-TD and health committee chair Jerry Buttimer, ex-junior minister Paudie Coffey and ex-TD Kieran O Donnell — had expressed an interest.
Mr Reilly and Mr Buttimer are widely tipped to be front runners for the position.
It is expected the move will be discussed once it has been made at a Fine Gael senators meeting this morning, before the Seanad meets at 2.30pm.
During the 2013 referendum on whether to scrap the Seanad, Mr Reilly said the upper house should be removed.
The Seanad will sit this afternoon to vote on the appointment of a cathaoirleach, likely to be Fianna Fáil’s senator Denis O Donovan. It will then stand down until next week when a leas cathaoirleach is appointed, with Fine Gael believed to be keen to promote Fine Gael senator Paul Coghlan to the role.
In the Dáil, a more complicated vote situation surrounding who should take up the leas ceann comhairle position may be discussed today or tomorrow, with strong indications Independent TD Mattie McGrath may ultimately succeed as a compromise candidate.
Meanwhile, Labour will announce its new public spokespeople this afternoon, including a number of former TDs no longer in Leinster House. Alan Kelly will become health spokesperson, with Seán Sherlock and Joan Burton taking up the public expenditure and finance roles.
Among the non-Oireachtas members also likely to be given positions are former bank inquiry chair Ciarán Lynch, ex-junior minister Kathleen Lynch, Michael McNamara, Joe Costello, and Emmet Stagg.