Several party sources said the leadership would announce the name this afternoon.
The candidate will then be formally ratified by the party's Ard Comhairle over the weekend.
Northern Ireland Deputy First Minister Martin McGuinness and former Stormont minister Michelle Gildernew are understood to be among the contenders.
Elsewhere, Senator David Norris is to appear on The Late Late Show on RTÉ tonight to discuss his renewed attempts to secure a nomination.
Mr Norris reactivated his attempts to secure a nomination by meeting Independent TDs yesterday.
He pulled out of the race in August over the controversy concerning his former partner Ezra Nawi.
The Fianna Fáil parliamentary party is to decide on Tuesday whether to allow TDs and Senators to nominate candidates.
Senator Labhrás Ó Murchú sought support from his colleagues to run as an Independent.
The backing of 20 members of the Oireachtas is needed to get on the Presidential ballot paper, which makes the signatures of the 33 Fianna Fáil TDs and Senators very valuable indeed.
The party will not be nominating a candidate of its own, but now it is coming under pressure to use those signatures to nominate Independent candidates.
Fine Gael's Gay Mitchell, Labour's Michael D Higgins and Independents Mary Davis and Sean Gallagher have been confirmed as candidates.