The Cabinet plans to reconvene later to discuss the possible sale of the State's stake in Aer Lingus.
Sources have said that the Labour Party members of the Cabinet may accept the sale as they believe now that the concerns of many TDs have been dealt with.
Ministers have discussed an expert panel report into the offer from IAG at this morning's meeting.
The Cabinet has now adjourned to allow for Dáil business this afternoon, but Ministers will reconvene at around 6pm this evening to continue discussions.
Meanwhile, Labour backbencher Joe Costello has warned that his party cannot support any deal, unless guarantees are given about jobs at the airline.
Deputy Costello has said that the future of airports like Cork and Shannon also need to be taken into account before any deal can go ahead.
"We have to protect Irish national interests in relation to this. So we will be pouring very closely over the proposals that have been made to ensure that they do that," said Deputy Costello.
"And if they do not do that then we have a unanimous vote from the Labour Party Conference not to accept a deal that does not comprehensively address those issues."
The Cabinet discussed an expert panel review of the revised offer from IAG at this morning's meeting.
Sources have said that the discussion was positive, but that they ran out of time as the EU Finance Commissioner is in Dublin and they had to get to Dáil business.
Earlier the Clare TD Michael McNamara said that if it wasn't a good deal, then he would vote against any sale in the Dáil.