Taoiseach Leo Varadkar has said former Fine Gael TD for Cork North Central Dara Murphy should pay back expenses he claimed if it is found that he broke the rules.
Speaking in Dublin Castle, Mr Varadkar said the Clerk of the Dáil could carry out an investigation into Mr Murphy who resigned as a TD yesterday.
Mr Varadkar said he agrees an investigation should be carried out.
That position is widely believed to be deputy head of staff for Bulgarian European Commissioner for Innovation Mariya Gabriel.
Mr Murphy has come under scrutiny in recent weeks following criticism over his Dáil attendance and the expenses he has claimed.
He has been largely absent from the Dáil due to a Brussels-based job with the European People's Party, the EU political grouping that Fine Gael is aligned with.
Mr Murphy has said he would "co-operate with any relevant statutory procedure that may be initiated" into his attendance and claiming of expenses.
Mr Murphy has insisted in recent days that he has been compliant with Leinster House rules following criticism from the Opposition.
A Fianna Fáil complaint against Mr Murphy was submitted to the Dáil's Members Interests Committee last week.
However, given that Mr Murphy is no longer a member of the Dáil, it is likely that the complaint will be referred to the Committee on Procedure and Privilege.
If accepted, it is open to the CPP to empower the Clerk of the Dáil to conduct a review and compile a report.
The first step, however, lies with the Dáil's Members Interests Committee, which is due to meet next week to resume its inquiry into voting irregularities by four Fianna Fáil TDs.
The Standards in Public Office said, meanwhile, that "... complaints about a person who has ceased to be a TD (eg resigned their seat), cannot be dealt with by... the Standards Commission".
The European Commission has declined to comment on the suggested inquiry into Mr Murphy's attendance and expenses record at the Dáil while working as both a TD and also for the EPP.
Chief spokesperson Eric Mamer told RTÉ News: "As a rule, we do not comment on national procedures such as this parliamentary complaint."
Trust in politicians at an all time low - McEntee
Meanwhile, Minister of State for European Affairs Helen McEntee has said that trust in politicans is at an all time low.
She was speaking in Washington and responding to questions about Mr Murphy, and said that every TD has to answer for themselves. She said that Dara Murphy has been asked to show that he worked within the rules and regulations of the Dáil.
"If anyone operates outside of the rules of the Dáil then obviously there would be repercussions," Ms McEntee said.
She added that Dara Murphy has said he will respond to questions and that he needs to be given time to do that.
Ms McEntee said that, in general, trust in politics is at a low point and it is up to politicians to show people they are working to represent them the best way they can.
"There have been a number of incidents recently that have brought public trust in politicians down to an all time low," she said.
Additional reporting Brian O'Donovan
