Minister for the Environment Phil Hogan has said it is too early to say if a by-election will be held in Dublin West on 23 May, along with the Local and European Elections, or in the autumn.
The seat in Dublin West has come up following the resignation of Independent TD Patrick Nulty.
However, Mr Hogan said because of changes in the political reform agenda, the by-election must be held within six months of the vacancy occurring.
Mr Nulty announced his resignation from the Dáil last night after he admitted he sent inappropriate social media messages, including one to a teenage girl.
He has been a TD in Dublin West for just over two years.
His dramatic resignation came last night as the Sunday World newspaper prepared to publish claims that he had sent lewd messages on Facebook, one of them to a 17-year-old girl.
It is also reported he sent a message to a woman telling her to wear a skirt the next time she attended his constituency clinic.
Mr Nulty admitted he had sent inappropriate messages, which he said were sent when he was under the influence of alcohol.
Mr Nulty resigned from the Labour Party last year. He had won a by-election for Labour in November 2011, but voted against the Budget just six weeks later.
His departure from Leinster House will be officially confirmed later this week.