The Fianna Fáil parliamentary party will meet later today to discuss the ongoing with the Ceann Comhairle.
It has not yet known whether Sean Barrett made contact with the party leader Micheál Martin as expected last night.
The Ceann Comhairle said yesterday both Sinn Féin and Fianna Fáil are entitled to question his decisions, but did not withdraw his comments alleging the Opposition was "out to get him".
A number of Fianna Fáil members are said to be in favour of tabling a Dáil motion of no confidence in the Ceann Comhairle.
Public Expenditure Minister Brendan Howlin has warned the opposition not to seek to “humiliate” the office of Ceann Comhairle.
Minister Howlin said this morning that the controversy over Mr Barrett’s comments last week is now “moving in a direction” and that people “should reflect on their position”.
“I hope there will be a situation today where the very hard work and, I think, the really good job being done by Sean Barrett is recognised,” he said.
“The one thing I would ask everybody to avoid is – there should be no seeking to humiliate the office of Ceann Comhairle, it’s far too important a job for our democracy.”