Sinn Féin members overwhelmingly voted against giving members a free vote on abortion at their ard fheis over the weekend.
There were impassioned speeches on both sides as the party debated whether members should be allowed to vote in the Dáil in accordance with their conscience on the issue of repealing the Eight Amendment.
Fianna Fáil sources say Mr Tóibín, who represents the Meath West constituency, could be approached about joining the party.
Fianna Fáil made overtures to Mr Tóibín in 2013 when he was suspended from Sinn Féin for six months after voting against the party position on the Protection of Life during Pregnancy Bill.
At the time, Mr Tóibín cited “major policy differences” as a reason for not joining Fianna Fáil. However, over the weekend, a number of Fianna Fáil sources questioned whether Mr Tóibín’s views on policy and issues are that different.
However, another source in the party said that, given that both Mr Tóibín and sitting Fianna Fáil TD Shane Cassells are both situated in the same area of the constituency, it is unlikely that he would be approached.
Another Fianna Fáil member said there was “absolutely no way” Mr Tóibín would be brought into it.
Instead of giving a free vote to members, Sinn Féin delegates passed a motion stating: “The party accepts the need for the availability of abortion where a women’s life, health, or mental health is at risk, and in cases of fatal fetal abnormality and in the cases or rape or sexual abuse.”
Sinn Fein deputy leader Mary Lou McDonald told delegates that the party would not “cop out” by allowing individual TDs and senators a free vote.
The Government has hinted that a referendum on the matter will be held next May or June.
Mr Tóibín spoke in favour of offering “some flexibility on the issue”.
He claimed that the party’s position has changed three times on the issue of abortion and that Sinn Féin stance on repealing the Eight Amendment had been different when he joined.
Mr Tóibín said: “The right to life is the primary human right. You cannot cherish all the children equally if you do not give the right to life to all the children.”
He said it would be “political kryptonite” if Sinn Féin were to back any law which appeared similar to the British abortion act.
Mr Tóibín also claimed that, in Britain, a “shocking” 97% of children who are diagnosed with Down Syndrome in the womb are aborted.
In recent weeks, Mr Tóibín has been contacted by party HQ after he claimed the Oireachtas committee on the Eight Amendment is biased.
Ms McDonald said the free vote is “nothing to do with freedom of conscience and everything do to with political expediency”.
Cork North Central TD Jonathan O’Brien said believing there should be access to abortion in Ireland “does not make me pro-life or pro-choice, it makes me a realist”.