Finance Minister Paschal Donohoe has become the latest to weigh in with questions around Tony Holohan's new role.
The outgoing Chief Medical Officer is leaving his post to take up a position with Trinity College Dublin (TCD).
Dr Holohan will take up the position as Professor of Public Health Strategy and Leadership on July 1st.
However the change is an open-ended secondment, rather than a permanent move.
As such the Department of Health is to continue paying his salary of more than €187,000 - even though he will not be working there.
Minister Donohoe told The Hard Shoulder some members of Government were kept in the dark.
"We were not aware of this particular announcement when it was made.
"I think there are some questions that do need to be answered about the nature of the contract, and how this decision was communicated."
However Minister Donohoe says he believes it is better for Dr Holohan to remain in the civil service.
"I would far rather that Tony Holohan be retained in our public service, and help us think about the future, and educate us for the next big health shock that we may have maybe in a few generations' time.
"There are issues that will be answered by the Department of Health in relation to this.
"I would prefer to have Tony Holohan in an educational role, in our public services, where we can benefit from his experience ands expertise".
And he says the Department of Health wants this role to be filled.
"What the Department of Health have indicated is, given the importance of learning about pandemics, and how we can prepare for other challenges to public health in the future, they are funding it.
"But I do accept... that this could have been communicated in a different way.
"And there are issues in relation to the contract, it's duration, that do require further clarification".
Earlier, Public Expenditure Minister Michael McGrath also said questions need to be answered.
"There are characteristics of this that are unusual and it could have been handled better in the sense that, when confirmation was provided that Dr Holohan was leaving the Department of Health, I think the assumption was that it was a permanent move.
"Secondments by their nature are generally temporary in nature, this particular one is open-ended in nature - which is unusual.
"So there are questions that arise there that will have to be answered", Minister McGrath said.
On suggestions of a mini budget to help with the cost of living, Minister Donhoe says a lot has already been done.
"We've already put in place nearly €2bn worth of measures... between Budget Day changes that we've made and two different packages that we've announced since the year begun.
"Sinn Féin are making the point that we should be doing more because we have a surplus today.
"As the year goes on we're going to be borrowing - we're going to finish the year having to borrow to fund the gap between what we are taxing and what we are spending.
"And we should not use borrowing to fund changes in taxation, as is being suggested by Sinn Féin."