Labour ups the ante in battle to win role of EU Commissioner
His comments illustrate the growing divide between the coalition parties over who should get the coveted €250,000 a year job, as Mr Hogan has long been seen as the front runner for the post.
Mr Costello, the Minister of State at the Department of Foreign Affairs, told RTE's 'The Week in Politics', that Mr Gilmore's track record in Foreign Affairs makes him the ideal candidate for the job.
"Absolutely he should be considered. I think of all of the people available, I think he has the strongest credentials," Mr Costello said.
He said Mr Gilmore's experience during Ireland's EU presidency puts him in a strong position for the post and to secure a significant portfolio.
Since his resignation in the wake of the disastrous local and European elections on May 23, the Labour Party has been pushing the case for Mr Gilmore to become the next EU Commissioner.
Mr Gilmore, himself, has publicly expressed an interest in the post but said it is at the discretion of the Taoiseach.
Another name to emerge for the post is MEP Mairead McGuinness, which would mean Mr Gilmore and Mr Hogan could lose out.
Separately, Transport Minister Leo Varadkar has said only Mr Kenny would decide who stays in or goes from Cabinet.
Mr Varadkar has long been seen as the front runner to replace the embattled James Reilly as Health Minister in the pending reshuffle.
Government sources suggesting the Taoiseach wants a "safe pair of hands" for the high-profile portfolio, with Mr Varadkar seen by some as "too unpredictable."
Speaking to Newstalk, Mr Varadkar said: "It is the Taoiseach's prerogative to select the Cabinet. It is a bit like the manager selecting the football team or a general deciding the mission for his troops.
"It is entirely his prerogative and I think there is to be a lot of speculation. The only person who knows who will be where is Enda Kenny and he'll make his announcements when he is ready."
There were some conflicting signals over the weekend as to when the reshuffle will happen.
If Joan Burton is elected leader of the Labour Party, as expected, then some have suggested she will want to "hit the ground running" and make her changes quickly.
However, senior Fine Gael sources said last night that the process "will not be rushed" and would take a bit longer than the previously expected announcement date of July 8.