Sinn Féin believes medical testing must be done in Ireland in order to ensure it is up to standard.
The Oireachtas Committee on Health is due to question Dr Gabriel Scally on his report on the Cervical Check review.
More than 200 women missed out on earlier intervention because of a delay in the detection of their cancer.
Sinn Féin Health spokesperson Louise O'Reilly said it is time to take control of the tests by making sure they happen at home.
Ms O'Reilly said: "But I also want to hear from Dr Scally, whose views on the outsourcing and how we can chart a course back to repatriating that work into the state, because I believe the labs should be based in Ireland. I think that's the only way we can guaranteee control over where the tests go."
The party also said questions need to be answered about how the testing of Irish womens' cervical smears were outsourced.
Ms O'Reilly said the quality of testing had clearly suffered in a drive to save money.
She said: "We know that the smear tests that were taken here in this State were taken to America, and we know that they were then re-outsorced to other labs in places like Honolulu.
"We know that there was no oversight by the HSE and I want to know that he (Dr Scally) has spoken to the people involved and that there is an understanding that that cannot happen again."