The proposal, first made in a letter to the Taoiseach by Cork North West deputy Michael Creed, would allow for the legislation on abortion to be reviewed after a number of years.
If it had led to an "opening of the floodgates" then the law could be looked at again, Mr Creed wrote in a letter released to RTÉ News under the Freedom of Information Act.
The call has been backed by Junior Minister Lucinda Creighton who said it was constructive and sensible and should be considered by Cabinet.
Cork South West TD Jim Daly said he met with the Taoiseach recently to urge him to accept this clause.
He added that it was a popular proposal and would ensure that abortion would not become widely available here.
Fine Gael TD for Mayo John O'Mahony also said he would welcome such a clause.
However, he said he did not believe a "sunset clause" was required.