Three Labour TDs have expressed interest in putting their names forward for the role of leader.
Speaking on RTÉ Radio's Morning Ireland, Mr Gilmore said Pat Rabbitte's decision to step down had first to be absorbed.
Mr Gilmore, who is the party's spokesperson on the Environment and Local Government, said that he has been discussing the situation with colleagues.
The Labour Party's spokesman on Foreign Affairs, Michael D Higgins says he would be happy to support Mr Gilmore in a leadership race.
Mr Higgins said that he would not be going forward but that he would have to see whom he would vote for as leader.
He said he had supported Mr Gilmore before and would be happy to do so again. He said he admired his skills as a negotiator and spokesman on environment.
While Tommy Broughan, who is the party's spokesperson on Communications, Marine & Natural Resources, has also indicated his interest in the leadership.
He said he did not think anybody who had served in the Dáil would turn down that situation.
Labour spokesperson on Finance, Joan Burton, has confirmed that she is also interested in leading the party.
Ms Burton says she is interested in being leader, but will not declare her candidacy until she has further discussions with her colleagues.
She said the challenge facing Labour now was to become a campaigning party on the floor of the Dáil and within constituencies.
Meanwhile, Labour TD for Longford-Westmeath, Willie Penrose, has said he is not considering running as a candidate in the leadership contest.
He says he has been approached by colleagues to put his name forward but at this stage he does not believe he will run.
The party's National Executive is to meet next week to fix a closing date for nominations in the contest.
It follows Mr Rabbitte's surprise resignation yesterday after five years as Labour leader.
His successor will be elected by a postal ballot by all full members of the Labour Party.
That procedure is likely to last well into October.
Mr Rabbitte, who stepped down with one year of his term remaining, said he did so to give his successor a chance to settle into the position before the European and local elections in 2009.
