MINISTER Brendan Howlin said that the majority of Cabinet members would be in support of same-sex marriage.
A Cabinet meeting will discuss the issue of approving a referendum on same-sex marriage today.
However, it is expected that it will not be voted on until 2015 at the earliest.
Minister for Public Expenditure Howlin said that the Government was aware that the issue was of huge importance for Irish people.
"The convention was very strong in its recommendation that there should be a referendum, that's probably the view of the majority of the Cabinet," he said.
Minister Howlin said that there will obviously be divergent views on the controversial subject.
"All the issues are challenging, but we've come a long way in this country," he said.
"When we introduced legislation for civil partnerships, second stage of that was passed without a vote in the Dail. I think Irish people in all the opinion polls have indicated support on this issue and they should be given the opportunity, when it's practical, to express their views."
Speaking on his way into the Cabinet meeting this morning Tanaiste Eamon Gilmore said he hoped there would be a referendum "in the lifetime of this government".
"It is important that we win this referendum," he said.
"It is an important issue and we know from referenda on social issues before that it is important to do some preparation before the referendum is held."
The constitutional convention voted last April to recommend a change in the constitution to allow for same-sex couples to have a full civil marriage and not just a civil partnership.
Minister for Justice Alan Shatter said yesterday that it was unlikely another referendum would be held before 2015 following the defeat of the Seanad referendum last month. "I suspect the general public are suffering from referendum fatigue," he said.
"Having been in the Dáil for many years, I can't recall so many referenda taking place within such a short space of time on so many very important issues.
"It may well be the case that 2014 is a referendum-free year and that if further referendums take place, possibly they should be in 2015."