Ministers are gathering at Government Buildings for the first Cabinet meeting after the summer break.
The future of Anglo Irish Bank is expected to dominate discussions after the Greens declared they want it wound up in four or five years.
But the Finance Minister Brian Lenihan is standing firm that a longer wind-down offers best value to the taxpayer.
Mr Lenihan will push for the splitting of Anglo into a good and bad bank - with the latter accounting for 80% of the balance sheet - effectively being wound up in seven to 12 years.
On his way into the meeting Taoiseach Brian Cowen hinted the Greens demand would not be met.
It follow concerns after a report was published in the International Herald Tribune this week debating the possibility that Anglo Irish Bank may sink the country financially.
It is expected Fianna Fáil will resist the Greens' proposals, despite the issue being constantly raised by the public with politicians.