The 20 TDs being lined up for talks
Fine Gael leader Enda Kenny has 50 guaranteed votes, plus the already pledged support from Tipperary TD Michael Lowry.
With Seán Ó Fearghaíl set to abstain due to his role as Ceann Comhairle, Fianna Fáil leader Micheál Martin has 43 guaranteed votes on April 6.
This means Mr Martin needs eight additional votes to draw level.
Both parties are realistically eyeing up the support of around 20 TDs.
This cohort includes the six-person Independent Alliance, as well the Social Democrats, who have three TDs, and the Green Party, which has two.
The support of so-called 'old Independents', such as Maureen O'Sullivan and Thomas Pringle, could prove to be crucial.
Talks will also take place with a group of Independents which has now been termed the 'Rural Alliance'.
The five deputies - Mattie McGrath, Denis Naughten, Noel Grealish, Dr Michael Harty and Michael Collins - all abstained in the votes last week.
Deputies Michael Healy-Rae, Danny Healy-Rae and Katherine Zappone are also on the radars of the two main parties.