The party led by Mary Lou McDonald is supporting repeal of the Eighth - but currently opposes the legislation proposed to take its place.
Without the backing of Sinn Féin it is extremely unlikely the laws being proposed will get through the Dáil, even if the public back the referendum.
The latest Irish Independent analysis of support for the 12-week proposal shows 57 TDs in favour and 73 against, including Sinn Féin's 23.
Unlike in Fine Gael and Fianna Fáil, the Sinn Féin hierarchy has decided not to allow its public representatives vote with their conscience on the issue.
Instead they are tied into the party position, which only supports terminations in cases where a woman's life, health and mental health is at serious risk or in grave danger, and also in cases of fatal foetal abnormalities and cases of sexual abuse and rape.
Ms McDonald has indicated a change of policy may be forthcoming on foot of an internal party review - but this may not take place until after the referendum.
And it's understood there are concerns the issue could split the usually united party as many members are strongly in favour of retaining the Eighth.
The Children's Minister, who is to the forefront of the repeal campaign, said it would help the political dialogue if Sinn Féin moved swiftly to review its position.
Referencing the opening statements in the Dáil debate on the topic last week, Ms Zappone said she "listened very carefully to the very strong words of Mary Lou McDonald" and also Dublin Mid-West TD Eoin Ó Broin.
"I do know that some of their colleagues have changed their minds in light of the facts, the evidence, the legal testimony.
"I hope they can do that. I think it would be good for the party and also be good for the campaign," she said.
At the same time Ms Zappone said she is not concerned that many politicians are continuing to stall when it comes to declaring their position on the issue of 12 weeks.
"The politicians, my colleagues, some of them are continuing to listen to the debate, to consider the proposals that government is putting forward.
"I think they'll make up their minds well within the next short period of time in order for us all to go out present to the people what we believe," she said.
Among the 28 TDs who have yet to give their view are Ms Zappone's Cabinet colleagues Michael Ring, Heather Humphreys and Denis Naughten.
Meanwhile, the Pro Life Campaign has said comments made by Taoiseach Leo Varadkar while in the United States "should give pause for thought to everyone who believes unborn babies are deserving of protection in the law".
Mr Varadkar indicated his belief that unrestricted abortion could be voted through the Dáil by the end of the year if the referendum is passed.
Dr Ruth Cullen of the Pro Life Campaign said: "In one sense the Taoiseach was stating the obvious when he said that unrestricted abortion in the first three months of pregnancy would be in place quickly if repeal happened.
"But what his comments certainly show is that what the Government is proposing is abortion on demand and nothing else."