The party has sent a discussion document to other parties
One of the Fine Gael negotiators in talks to form a government says nobody wants another election.
The party says it is intensifying talks with Independents and small groupings in an attempt to form a minority government.
But the party says it will not be making contact with Fianna Fáil until it sees what its position is with these groupings.
Meanwhile, Independent Danny Healy-Rae has criticised other TDs for being "hurlers on the ditch" when it comes to forming a government.
Fine Gael is meeting for a second day for talks with 15 independents and the two Green TDs.
But with suggestions from some of the Independents the talks could drag on forever at their current pace, Fine Gael negotiator and acting Health Minister Leo Varadkar says they want to put a stable coalition together.
Acting Justice Minister Frances Fitzgerald says they are respecting the vote of the people by engaging in this process.
While acting junior finance minister Simon Harris says it is still way too early in the process for Fine Gael to open discussions with Fianna Fáil.
As they arrived brothers, Danny and Michael Healy-Rae criticised up to 40 TDs from Sinn Féin, the Anti-Austerity Alliance and others for not taking part in talks.
Talks will continue today and throughout the rest of the week - ahead of the return of the Dáil in eight days time for the next attempt to form a government.
The housing crisis is expected to top the agenda today.
Fine Gael has reportedly offered the first concrete deal to Independents and smaller parties, as they try to form a minority government.
The party sent a discussion document to those taking part in talks last night.
The Irish Examiner claims it contains promises to create a new Minster for Housing, an eight-week housing action plan and suggests ways to cut down on empty homes.
It is also said to include a commitment to examine mortgage reforms for struggling families and tax relief for landlords who accept rent supplement from tenants.
However, it is believed that none of the 37 separate points have been costed.
Fiach Kelly of the Irish Times told Newstalk Breakfast earlier a change in VAT could also help.