The abortion bill is on the 'A list', meaning it is one of those being given highest priority.
However, the legislation has yet to be finalised and is unlikely to be for another few weeks.
While sources said the bill would be published by the summer, it is unclear whether it will be passed.
It is likely the bill will not pass through the Oireachtas until the autumn at the earliest.
It comes amid increasing tension in Fine Gael on the issue, with some TDs calling for a "sunset clause" to be inserted into the legislation.
Cork North-West TD Michael Creed wrote to Taoiseach Enda Kenny requesting the clause, which allows for the law to be scrapped if there was an unexpected surge in terminations.
Those opposed to abortion have consistently expressed worry that any new law would "open the floodgates" to abortion on demand. In particular, they are concerned about allowing for the threat of suicide, which, they fear, could lead to widespread abortions.
Some in Fine Gael say the sunset clause will guard against this by reviewing the legislation after a few years.
European Affairs Minister Lucinda Creighton is one of those backing the clause, but it has been received coolly by Labour.
Communications Minister Pat Rabbitte said he wasn't sure if such a clause was appropriate.
Justice Minister Alan Shatter said he believed a review would be appropriate, but backed away from the suggestion of a sunset clause.
"I'm not sure to refer to it as a sunset clause is appropriate. A sunset clause in legislation normally means that after a specified period of time, legislation lapses," he told RTE .
"I don't think that's what my Fine Gael colleagues are suggesting. I think what's appropriate is legislation must be reviewed and a review is necessary because no matter what legislation the Minister for Health publishes to address this sensitive area that affects so many people, there are issues he can't address."