Sinn Féin Leader Mary Lou MacDonald has said that a motion of no confidence in the Health Minister will not succeed without the backing of Fianna Fáil.
It comes as documents emerged showing Mr Harris was aware of a possible €400m overrun at the National Children's Hospital last August, seven weeks before he told the Taoiseach or the Finance Minister.
A memo is due to be brought to cabinet outlining the savings needed by other departments to pay for the additional costs.
Ms MacDonald said that a confidence motion in Mr Harris will only be brought if they get the backing of other parties.
She said: "I have no confidence in Simon Harris. I believe he needs to go. We've made that position clear.
"I have no difficulty moving a confidence motion but we want to know that it will succeed and it is Fianna Fáil, not Sinn Féin, that's keeping Simon Harris in office."
Meanwhile Taoiseach Leo Varadkar has said that he has total confidence in Mr Harris.
Mr Varadkar said that even if Simon Harris had told him about the overruns earlier, he would have instructed him to do exactly what he did.