Fine Gael and Fianna Fáil could agree a joint government policy document either this week or next, Leo Varadkar has said.
The Fine Gael leader was speaking ahead of another meeting between the parties this afternoon, which has been described as "positive".
Both sides say they will keep the policy discussions confidential and will be in contact over the next few days.
Mr Varadkar said that once agreement on the policy document had been reached, approaches would then be made to the Green Party, the Labour Party and the Social Democrats to seek their support.
Fine Gael and Fianna Fáil are likely to hold a further meeting before the end of the week.
"We believe what's required is a government that is going to last four to five years, which can deal with this crisis, the recovery, and putting our society and economy back together when we've got past this health crisis," Mr Varadkar said.
He said this would require the support of a third political party and some independent TDs as well.
Mr Varadkar added that this entire process would take "a few weeks" and the number one priority was dealing with the Covid-19 crisis.
On the question of whether he would remain on as Taoiseach in a new government, he said this was something that was being discussed with Fianna Fáil.
He pointed out that Fianna Fáil had "slightly more seats" than Fine Gael and said his party recognised this.
But he added his focus is not on what job he will have in a few weeks' time, but on dealing with Covid-19.
The Green Party reiterated its position today that it would only agree to be part of a national unity government.