He said if elected taoiseach next week as expected, “the cabinet will be appointed by me on the basis of what’s best for the country”.
Mr Varadkar said he is also considering a radical shake-up of departments.
“That is something that is under consideration, the restructuring of Government departments to reflect what I believe are the particular needs into the future.”
It has been widely speculated the two finance departments could again be united amid the further likelihood of splitting up the department of justice and establishing a separate home affairs department.
Other changes to reflect the challenge of Brexit are also being considered, senior government sources said.
Mr Varadkar was pressed as to likely inclusions in his first cabinet but declined to comment on a request from Simon Coveney not to penalise those TDs and ministers who opposed him.
The housing minister, earlier this week, had warned Mr Varadkar against dropping Minister for Health Simon Harris, who is a key supporter of Mr Coveney.
In response, Mr Varadkar would only say that he had not made any decisions yet, leading some to think that Mr Harris’s job is at risk.
He said he would take “a degree of regional balance and gender balance” into account when selecting ministers, but that the “core issue” was “trust”.
“Anyone who runs a cabinet, and anyone who heads up a government, who heads up a football team, needs to know that everyone on that team is going to be fully behind your programme,” he said.
Having previously said he did not trust Fianna Fáil, Mr Varadkar said it would be possible to have a good relationship with Micheál Martin. Asked repeatedly if he could now trust them, he replied: “We’re not going to be best friends, and we’re certainly not going to be in coalition, but we are going to have a good working relationship.” Of his previous criticisms of Fianna Fáil, Mr Varadkar said he was starting a new role, and it was “an opportunity to start afresh”.
He said he “had to get back to Fianna Fáil and the Independents on specific issues” but talks had gone smoothly. He is scheduled to meet the Independent Alliance again on Sunday.
The Fine Gael leader said he had agreed with the Independent Alliance that the Government would look at the possibility of free votes on specific issues “on a case by case basis”. He said there “could potentially” be a free vote on new drink-driving legislation.
Mr Varadkar said he had not had any discussions with Independent TD Michael Lowry, as of yet.