Leo Varadkar has warned that there will be "more disappointments than appointments" as he puts together his cabinet.
But the new Fine Gael leader has said he is not yet considering ministerial appointments, because he is still focussed on securing the support of independent TDs for him as Taoiseach.
He says he is giving some thought to restructuring government Departments, but will not say which ones.
And he says he hopes his colleagues will understand that they cannot all get cabinet seats.
He said: "I'd hope that anyone who is not appointed does not think they have lost out forever."
Leo Varadkar has said he has no plans to speak to Michael Lowry to seek his support for the Government.
The new Fine Gael leader said there was no agreement with the Tipperary TD, and he did not plan to meet him.
He added he had made good progress in talks with the eight independent TDs who supported Enda Kenny's Government.
"What I've said that any understanding that existed prior to now with the outgoing Taoiseach I am happy to honour, but there's no formal agreement in place (with Michael Lowry)," he said.
Leo Varadkar is spending time garnering support ahead of forming his new administration next week.
He has been meeting with Independent TDs and Ministers, and Fianna Fáil leader Micheál Martin.
Independent TD Dr Michael Harty has met the Taoiseach-elect with Denis Naughten and Katherine Zappone to discuss national and local issues. They first met as a group, followed by a 10-minute individual session for each of the independent TDs.
Minister for Children Katherine Zappone asked Mr Varadkar to speed up preparations for an abortion referendum.
Deputy Harty said that among other issues, including facilities at Ennis Hospital, "I also spoke to him in relation to a VAT refund scheme for charities, where charities collect money and buy equipment, but have to pay VAT on that equipment, which seems quite unfair.
"He was quite receptive to that."
Mr Varadkar has said the meetings are focused on legislation that needs to be prioritised, improving the working of the Dáil, and accelerating the implementation of commitments in the Programme for Government.
He said: "All of the meetings were useful and I feel that we are going in the right direction."
He is expected to be officially named as Taoiseach when the Dáil returns next Tuesday, June 13.