The Minister for Media has said she would like to remain in her current role in order to make a decision on the future funding of public service media before the Dáil summer recess.
However, Catherine Martin said this will be in the hands of the new party leader, but she is hopeful that she will remain as Media Minister.
Ms Martin said both candidates running for the leadership - Roderic O'Gorman and Pippa Hackett - know about the importance of making a decision on the future funding of RTÉ.
The minister also said any large exit payments for staff leaving RTÉ should be the exception rather than the norm.
Asked about an anticipated payment of €400,000 to a senior figure leaving the organisation, the minister said she expected RTÉ "to take all advice and recommendations from any independent mediation body that is being used."
More importantly she said it was important that RTÉ "would get value" in this process because "at the end of the day they are publicly funded."
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Minister Martin said she understands that the process around this exit package is still on going and no figure has been decided yet.
The outgoing deputy leader of the Green Party said Eamon Ryan told her many months ago that he intended to step down as party leader and not run in the next general election.
She said that she would not be endorsing any leadership candidate because for the moment she is still deputy leader until a replacement is elected.
She said the party leader or deputy leader never endorse a candidate in internal elections.
Nominations open for Green leadership contest
Nominations for the Green Party leadership contest opened this morning and will close at 9pm on Monday.
It followed the announcement on Tuesday by Mr Ryan that he is to step down as party leader.
The Green Party’s executive finalised the details of the leadership election last night.
The new leader will be announced on 8 July, with the Dáil recess commencing later that week.
The Green Party said it will send its members information about the deputy leadership election in the coming days.
Amid the flurry of activity within the smallest Government party, Taoiseach Simon Harris urged his party’s TDs, Senators and MEPs to push back hard against talk of an early general election.
Mr Harris told a meeting of the Fine Gael parliamentary party that the Government would deliver a budget which will result in meaningful changes for people.
'Two excellent candidates'
Green Party TD Brian Leddin has said he is happy that "two excellent candidates" are running, adding that it is important the party has an election.
"Although I am supporting Pippa Hackett for leader, I will be happy to support Roderic O'Gorman should he win," Mr Leddin said, "and I told Mr O'Gorman this at the weekend".
"This is a judgement call and my own belief is that Pippa Hackett offers the party the best chance of winning votes and seats in the general election," Mr Leddin added.
Speaking on RTÉ's Morning Ireland, he said that whoever is elected will have a mandate to bring the party forward and "I think every member will get behind them".
Green Party councillor Janet Horner said she believes Mr O'Gorman has demonstrated the qualities needed to be the next leader of the Green Party.
"We have seen him time and again step up to leadership roles," she said.
"Roderic O'Gorman has experience at every level, she said, and I think the party needs that continuity.
"In addition he is a trusted and personable colleague," Ms Horner added.
Green Party councillor Hazel Chu said she will support Minister O'Gorman, adding that he has more experience than Minister Hackett
Speaking on RTÉ's Today with Claire Byrne, Ms Chu said the new leader will have to sell the message to urban voters and those in rural Ireland that there is a climate emergency and action is needed.
On the same programme, Cork Green councillor Dan Boyle said he was not ready to publicly declare who he is backing.
