Director of Elections for the party, TD Matt Carthy, and sitting TD Pauline Tully, have already been selected as candidates and Monaghan Cllr Cathy Bennet is expected to be selected in a second convention on Sunday night.
Cllr Bennett is currently the Cathaoirleach of Monaghan Municipal District and is the chairperson of County Monaghan Women’s Assembly.
While other candidates may also put themselves forward in the selection convention on Sunday night, Cllr Bennet is understood to be the frontrunner.
She proposed Mr Carthy as a candidate for the party at the first selection convention in September and topped the poll in the Monaghan local electoral area in June.
The party fared well in the area in the local elections, going from six to eight seats in Monaghan and gaining two councillors in Cavan.
The party is seriously targeting a third seat, a party source said, as the departure of Fine Gael’s Social Protection Minister Heather Humphreys is a “game changer”.
The Cavan Monaghan constituency, which is a five seater, usually sees two TDs elected from Cavan and three from Monaghan, a source said.
Sinn Féin is hoping for Ms Tully to be one of the so-called Cavan TDs and for Mr Carthy to keep his seat in Monaghan and get Cllr Bennet over the line.
Mr Carthy is the party’s Director of Elections for Sinn Féin in this year’s general election. There were previous suggestions the party was aiming for three seats in the constituency, where it currently has two TDs.
Fianna Fáil holds two seats with Niamh Smyth and Brendan Smith.
Meanwhile, the party is expected to lose its seat in Laois after TD Brian Stanley announced on Thursday he would be running as an independent.
Sinn Féin have not responded to queries on whether they have selected a candidate yet, after indications it would do so this week. The only elected representative for the constituency is Cllr Caroline Dwane Stanley, Mr Stanley’s wife, who is not expected to run in the general election.
In his first public media comments on Friday, Mr Stanley said party leader Mary Lou McDonald’s handling of the controversy surrounding his resignation last month was “appalling”.