The chairman of the Public Accounts Committee (PAC) has publicly urged Michael Noonan to appear before the committee for questioning.
Sean Fleming says the Finance Minister is "a link in the chain" surrounding concerns about the sale of NAMA's Northern loan book, known as Project Eagle.
A spokesman for the minister says he is considering the invite, but stressed that it was "not normal practice" for ministers to attend.
"The Department of Finance will cooperate fully with the PAC as the Department always does," the statement adds.
Sean Fleming says there are specific issued raised about NAMA that only the minister can address.
"I will stress that we will be asking him specifically in relation to his involvement in the Project Eagle sales process," he said.
"There's letters bearing his name, there are phone calls he was personally involved with, with people from NAMA and the Department of Finance in Northern Ireland, and he involved himself in the process".
Opposition parties have joined the calls for Minister Noonan to appear before the PAC.
Social Democrats co-leader Róisín Shortall described it as “an exceptional case and therefore requires an exceptional approach".
She also argued it would not be unprecedented for a minister to appear before the PAC, highlighting that “in December, 2011 the then Minister for Public Expenditure and Reform Brendan Howlin attended the PAC to brief the committee on the Public Service Reform Plan".
Yesterday Sinn Féin deputy leader Mary Lou McDonald claimed that “Mr Noonan, as Minister for Finance, failed to protect the interests of the citizens of this state. It now seems that he will try to avoid being held accountable for these failures by refusing to come before the Public Accounts Committee.
"Such a refusal by Minister Noonan would make his position untenable. Minister Noonan must appear before the PAC at the earliest opportunity to answer questions on this matter," she added.
Minister Leo Varadkar yesterday indicated his cabinet colleague will not appear before PAC and he accused the opposition of conducting a "witch hunt".
It was confirmed last week that a statutory inquiry is to be established to look into Project Eagle, with opposition TDs calling for the inquiry to also examine wider issues at NAMA.
The move followed a report by the Comptroller and Auditor General that claims the taxpayer lost as much as €220 million on the Project Eagle sale - something NAMA denies.
