Mr Donohoe is understood to have told the Cabinet that Ministers had thus far been able to examine the committee's report in a calm environment, which may not be the case during a referendum campaign.
Numerous Fine Gael Ministers referenced the difficulties in the party during the debate over the Protection of Life During Pregnancy Bill, which saw three TDs and one senator leave the party in the last Dáil.
In the absence of a full Cabinet decision, which won't be made until after the Dáil has debated the issue, he wants to focus his work on the recommendations of the Oireachtas Committee on the Eighth Amendment.
Both Ministers, however, told their colleagues they supported the Oireachtas committee recommendation allowing for abortion on request up to 12 weeks of pregnancy.
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.
Mr Varadkar said there were diverse views at cabinet during a discussion about the likely referendum on the Eighth Amendment.
Varadkar said today that he wished to hear the views of the Fine Gael parliamentary party. I know other parties are going to do the same.
Minister for Finance Paschal Donohoe did not make his views clear prior to Christmas but said yesterday that he supported the recommendations of the committee.
"For a lot of people, not just in cabinet, a lot of people in the country, the proposal to allow for the termination of pregnancies up to 12 weeks went further than many people would have anticipated", he said. The Dáil and Seanad will be discussing the issue next week.
"I don't believe that this is an issue that should be in our constitution", he said.
His colleague, Business Minister Heather Humphreys, said she wanted to consult with her voters in Cavan-Monaghan and particularly women on the matter. "And I particularly want to consult further with the women because at the end of the day it will be women who are most impacted on this issue".
Ministers were told that a referendum could be held in late May or early June.
Health Minister Simon Harris will present his plans for a referendum and the new laws that could come in.