The Chairman of Public Accounts Committee has said that its members will be inviting representatives of international companies to "come and explain" their taxation structures.
Speaking on RTÉ's Today with Seán O'Rourke, Fianna Fáil TD Seán Fleming said the committee would be deciding this week what companies to invite.
Mr Fleming said such companies should be encouraged to "take a more moral approach to their taxes", and that they should fear the damage that could be done to their brand by not doing so.
"They have to trade off saving tax with damaging their brand and I think that a financial decision most chief executives will have to make," said Mr Fleming.
"I think all these companies will want to protect their brand and that's why we will be issuing invitations to all these companies.
"They have appeared in the House of Commons and in Washington and Ireland shouldn't be afraid to ask these people to come in as well."
Meanwhile, Fianna Fáil's Finance spokesperson Michael McGrath has said that Ireland has taken big strides in relation to tax avoidance but more steps could be taken.
He said Revenue needed to appear before the Finance Committee and a number of hearings should be held on the issue.
Mr McGrath added that there was a need to make sure Ireland is not complicit with tax avoidance tourism.
In relation to a number of high-profile names mentioned in the 'Paradise Papers', he said there was an onus on every Irish person to insure they were paying their share.
He said Ireland should participate on an EU level on tax avoidance reforms, but he said this ongoing controversy should not be used as a cover to bring in consolidated corporation taxes.
Seperately, Sinn Féin's Finance Spokesperson has said the closing of 'double Irish' loopholes in 2014/2015, opened up other loopholes that allowed companies like Apple to benefit to the tune of billions of euro.
Speaking on RTÉ's News at One, Pearse Doherty said the loophole allowed 100% of capital allowance to be set against profit.
He said he believed the then finance minister, Michael Noonan, allowed this to happen because he knew there would be a massive onshoring of intellectual property.
Mr Doherty said there were serious questions to be asked as to whether another sweetheart deal has been done with Apple and other multi national companies.