Independent TD Mattie McGrath said he is willing to support the Fine Gael minority Government in return for their support for the Leas Ceann Comhairle job.
Mr McGrath is one of four contenders for the position with a vote scheduled for this week.
A vote was held in the Dáil last week but none of the four succeeded in winning the support of the majority of the House.
Fine Gael is now said to be willing to ask its candidate Bernard Durkan to stand aside and support Mr McGrath.
The party says it would expect the Tipperary TD to back the Government on key decisions.
Speaking to the Irish Times, Mr McGrath said he had voted with the party on a number of occasions including last week’s private members motion on workers rights.
He said: “I want this Government to work. I don’t want it to collapse. I will always vote with what I believe is right.
“I have been constructive and I have met with the Government chief whip on a number of occasions.
“I have voted with the Government, I have abstained on other occasions.”
Fine Gael is eager to have the support of a number of Independent TDs after its last vote in the Dáil on workers rights last week.
The two other candidates for the position are Fianna Fáil TD Pat "The Cope" Gallagher and Sinn Féin TD Sean Crowe.
If Mr Gallagher succeeds Fianna Fáil will have the hold the roles of Ceann Comhairle, the Leas Ceann Comhairle, the Cathaoirleach of the Seanad and the chair of the Public Accounts Committee.
