Ministers are considering a separate vote on removing the clause about a woman's place in the home
The Cabinet is considering holding a referendum to remove the offence of blasphemy from the Constitution.
It is one of two votes likely to take place in October.
The Minister for Justice Charlie Flanagan brought the proposals to his Cabinet colleagues this morning.
The line of the Constitution the minister wants removed is: "The publication or utterance of blasphemous, seditious, or indecent matter is an offence which shall be punishable in accordance with law."
Should Cabinet approve the plan, Minister Flanagan will introduce a bill to the Dáil with the aim of calling a referendum in October to remove the article.
It is likely to take place alongside another referendum to remove the part of the Constitution that states that without a woman's place in the home, the common good cannot be achieved.
They will probably be held in line with a Presidential election if there is one - but could go ahead on their own if nobody stands against Michael D Higgins.