Fine Gael could face a scramble for votes to pass the budget if Peter Fitzpatrick leaves the party this weekend.
The Louth TD is to meet his team and will make a decision on running as an independent candidate in the next general election.
In August, Mr Fitzpatrick announced that he would not be running in the next election as a Fine Gael candidate. He refused to say whether he would put himself forward as an independent.
Asked about the departure rumours surrounding Mr Fitzpatrick, Finance Minister Paschal Donohoe said he hopes he remains in the party.
If Mr Fitzpatrick does leave the party next week, it would put additional pressure on Mr Donohoe, who is hammering out the final details of Budget 2019. Given the tight Dáil figures, the Government would face the possibility of not passing the budget if it could not get his support as an independent.
Mr Fitzpatrick was one of Fine Gael’s most high-profile opponents of the referendum to repeal the Eighth Amendment, which may have led to his decision not to run for the party in the next election.
Speaking in Dublin yesterday, Mr Donohoe said: “As far as I know he is committed and still a member of the Fine Gael parliamentary party and I am hoping that continues to be the case.
“But of course as a member of the Oireachtas he has the right to make any decisions that he wishes in relation to his future.
“I would hope I would have the opportunity to continue with him in Fine Gael and I hope that will be the case.”
Mr Donohoe denied that rumours of Mr Fitzpatrick’s departure are a sign of emerging cracks within the party.
“It is clear to me that the Taoiseach is leading a very united parliamentary party,” he said.
Mr Donohoe was speaking as he unveiled Deirdre Duffy as his running partner in the next election in the Dublin Central constituency.
Ms Duffy worked as campaign manager for the Together for Yes campaign and is a qualified barrister.
Mr Donohoe said he is confident Fine Gael can win two seats in the constituency but is under “no illusion as to how demanding that will be”.
“This constituency is gaining a seat so it’s moving to a four-seat constituency so that’s a really important development,” he said.
“I don’t expect a general election to be for quite a while but when it does happen... I know the trick to doing it is you don’t target anyone else, you just work as hard as you can for yourself and for your constituents.”
Ms Duffy, who lives in Phibsboro and is originally from Cork, added: “I have just been part of a female leadership of one of the most, if not the most, successful political campaigns that this country has ever had.
“So I wouldn’t be putting my name forward on the ballot for Dublin Central if I didn’t think that I was going to win and that we could bring in two seats.”