Mr Varadkar said he is looking forward to the leadership campaign and wants to “turn Fine Gael into a fighting force again”.
It comes after Taoiseach Enda Kenny told a parliamentary party meeting that he would be dealing with the leadership issue on his return from his St Patrick’s Day visit to the White House.
Mr Varadkar confirmed that he had spoken with Mr Coveney ahead of this meeting last Wednesday.
“We’re in touch. We get on very well. We’ve known each other for years. We’re a similar age. We meet and chat all the time and the two of us are very determined to make sure that whatever the outcome is that the party’s united thereafter and that it can do well,” he said.
He said both were “of the view that the feeling of the vast majority of people in the parliamentary party was to avoid a motion of no confidence, avoid division and divisiveness”.
However, he said that no formal agreement had been struck between the two favourites to take over from Enda Kenny and ruled out a similar deal to that of Labour’s Tony Blair and Gordon Brown in the UK.
“We know each other, we talk, but we don’t have formal agreements or a joint strategy or anything like that,” Mr Varadkar told RTÉ’s Marian Finucane show.
A poll over the weekend put the Social Protection Minister and the Housing Minister within two points of each other with Mr Varadkar on 29% and Mr Coveney on 27%. Mr Varadkar said the formal campaign has not started and other senior party figures could not be ruled out of the race for leadership.
“I know the media focus is all on me and Simon, I think it is important to remind people that there are lots of other leading figures in Fine Gael too, people like Richard Bruton, Frances Fitzgerald, Paschal [Donohoe], Simon Harris and others.
“So I don’t think people should make the assumption that it’s all about us,” he said.
A spokeswoman for Mr Coveney said both men have offices on the same corridor so speak regularly and have a good relationship.
However, she said there was no formal meeting before the parliamentary party meeting last week.
Over the weekend it was reported that Mr Coveney told supporters that he would he would be making sure that Fine Gael would “draw a line in the sand” with Fianna Fáil on certain core issues and if they crossed that line he would be prepared to call an election.
Government chief whip Regina Doherty said the party was in a pre-contest phase.