The Taoiseach Leo Varadkar has said any proposal to reinstate the SSIA savings scheme has to be considered.
The Special Saving Incentive Account was launched more than 17 years ago.
They were a five-year scheme, which was topped up the Exchequer.
It gave taxpayers back €1 for every €4 they saved.
For example, if you lodged €100 each month to an SSIA, you were entitled to receive €25 each month by way of a tax credit.
SSIAs were opened from May 2001 to April 2002 and matured between May 2006 and April 2007.
The Governor of the Central Bank has proposed introducing something similar, but only if the economy continues to grow quickly.
Mr Varadkar said it is something the Government will examine.
"I think you have to consider any proposal like that, particularly if it comes from anybody as distinguished as the Governor of the Central Bank.
"Bear in mind what happened last time, though - the SSIA was initially quite successful in taking money out of the economy at a time when there was a lot of money in the economy.
"Bt when it was released it actually released a lot of money into the economy at the peak of the boom - and as a result, probably made the boom boomier and the crash deeper.
"So in terms of doing something like that, we've a different idea - and it's around encouraging and getting people to save more for their pensions."
Finance Minister Paschal Donohoe speaking to the media at Government Buildings | Image: Sam Boal/RollingNews.ie
While Finance Minister Paschal Donohoe said he was willing to look into it.
"There's a number of very helpful proposals and suggestions being put to me at the moment.
"I'll absolutely be considering the views in relation to (Central Bank) Governor Lane in relation to (SSIAs).
"The kind of proposal that he has put there stretches beyond decisions that you can make on Budget Day - it's something that could happen after the budget."
"I guess one of the htings that we would need to weigh up, though, is that if people are putting money into an account they would feel that they should have the ability to decide when they take the money back out of the account.
"And that would be one of the things that we would need to consider".
With reporting by Jack Quann
