The parties are aiming to reach a deal on issues such as housing and rent supplement
Fine Gael negotiators say there are now only "one or two" issues left to be agreed with Fianna Fáil.
During a break in negotiations, Leo Varadkar said there was "substantial agreement on almost all matters".
Fianna Fáil however says it is disappointed that a deal on housing supports has not yet been agreed.
It is describing the issue as the single most important one facing Ireland today.
Talks between the parties are continuing this afternoon, with hopes of a possible deal this evening.
Simon Coveney says almost every point of dispute has been resolved.
Acting Justice Minister Frances Fitzgerald said earlier there were several issues yet to be sorted.
But she said a final deal to allow a government be formed could be ready today.
Fianna Fáil say a deal will not be delayed as a result of controversial comments by Leo Varadkar yesterday.
He said it was 'not in the national interest' to suspend water charges, despite being part of the team that negotiated it.
Barry Cowen says that will not be raised today.
Fine Gael's Leo Varadkar denies that his comments yesterday - describing Fianna Fáil's policies as 'insane' - will scupper a deal.
The acting health minister said he does not think personal remarks are 'conducive' to agreement, adding that "today is about business".
It is hoped a new government can be set up in the very near future after an agreement was reached on the subject of water charges.
It is expected that charges will be suspended for nine months, while an independent commission will be set up to examine the issue.
Sinn Féin's Deputy leader Mary Lou McDonald says given the charges are to be suspended, people who paid water bill should be reimbursed.
She also reiterated calls for a constitutional referendum to protect water services in Ireland in public ownership.
"I don't like the fudge that they have arrived at," she said. "I think if you wanted clarity on the issue of water, the mechanism was to put the motion to the Dáil...and to make a clear cut decision".