The Independent Alliance is to meet with the Attorney General this week to consider a bill allowing for terminations in the cases of fatal foetal abnormalities.
The group had requested a free vote on the private members bill by Independents4Change TD Mick Wallace.
The five TDs - including Minister for Transport Shane Ross and Minister of State Finian McGrath - have been told the bill is unconstitutional.
However members are seeking a further meeting with the Attorney General to assess if they can abstain in the vote, which will take place on Thursday.
It is understood Maire Whelan has informed the Alliance Ministers they cannot support a bill that is unconstitutional.
Minister of State John Halligan said he accepts Ms Whelan's advice but the Alliance still wants a free vote.
He said: “I would find it hard to vote against the bill considering my position on this.
“I believe terminations should be offered in these tragic cases. I have to accept the advice of Attorney General and I have no reason to doubt it but we are still pushing for a free vote or at the least to be allowed to abstain.”
Mr Wallace's proposed legislation will mirror that presented by his colleague Clare Daly last year. The very specific piece of legislation allows for an abortion to take place in cases of fatal foetal abnormality.
Under the measure, two suitably qualified medical professionals – a perinatologist and an obstetrician – would be asked to in good faith to certify if the foetus is incompatible with life.
His Bill has the support of deputies Thomas Pringle, Ms Daly, Catherine Connolly, Joan Collins, Maureen O'Sullivan and Tommy Broughan.
It is also likely to attract support from Sinn Féin, Labour, the Social Democrats, the Green Party and the Anti-Austerity Alliance-People Before Profit.
Fianna Fáil members will be allowed a free vote but there are varying views within the parliamentary party on the issue.