Earlier this week Alan Kelly resigned as Labour Party leader, after losing the support of his parliamentary party colleagues.
In a statement, the Labour Party said the nomination process for the leadership will be open until 12pm on 24th March, after which if only one candidate is put forward they will be elected party leader.
Speaking on Saturday, Ms Bacik would not comment on the leadership election, only stating she would be consulting with party members over the weekend.
Ms Bacik, a long time Senator, was elected to the Dáil last July, after winning the Dublin Bay South byelection.
The party statement said a candidate may be nominated for the leadership by at least two Labour Oireachats members, or five party constituency councils.
If there is a contested election the party membership will vote, with polling to close on 22nd April.
The party’s executive board and parliamentary party met on Saturday, and “affirmed that Alan Kelly would continue in office as acting leader until a successor is elected”, the statement said.
Only TDs are eligible to contest for the leadership of the party. Other potential contenders, such as Duncan Smith and Aodhán Ó Ríordáin, ruled themselves out of the running for the position shortly after Mr Kelly announced he was stepping down.
Previously Brendan Howlin was elected as leader uncontested in 2016, as he was the only candidate to receive a nomination from the parliamentary party.