However, Mr Coveney, who is seen as being on the conservative side of Fine Gael, will miss today's meeting as he is now on a tour of Israel and Palestine.
The Taoiseach says allowing abortion without restriction for up to 12 weeks into a pregnancy may be a step too far for some people.
"It (the proposal) went further than many people may have anticipated, it certainly went further than I would have anticipated a year or two ago", he said.
It was a private and personal matter and there was a diversity of views in "almost every household in the country", Mr Varadkar added.
While Varadkar has said that his Cabinet would take a collective decision on whether to hold a referendum, he has said that ministers would be able to "dissent" from that.
British Prime Minister wants to cut all avoidable plastic within 25 years
The overall plan was "a cynical attempt at rebranding the Tories' image and appears to contain only weak proposals", she said. However, opposition leaders and environmental campaigners were quick to condemn the proposals as dangerously insufficient.
At its first cabinet meeting of the year yesterday the government spent two hours debating the recommendations of an Oireachtas committee.
However, Minister of State at the Department of Finance Patrick O'Donovan said he had a "different view".
Irish justice minister Charlie Flanagan has indicated he supports the repeal of the eighth amendment, saying he did not believe it was an issue that should be in the constitution.
The Taoiseach confirmed before Christmas that all Fine Gael Oireachtas members will have a free vote on any referendum proposal when it goes before the Dáil and Seanad.