The bank, favoured by property speculators and developers before the 2008 crash and since rebranded the Irish Bank Resolution Corporation (IBRC), has cost the state €28bn (£24bn).
Government sources claimed the plan, if accepted by the ECB, would be "very advantageous" for Ireland.
The coalition has been battling with European leaders and officials in Brussels and Frankfurt since taking power in early 2011 to cut the cost of the country's bank bailout.
The Irish Government has been in long-running talks to cancel a repayment scheme of £3.1bn (£2.6bn) a year until 2023 for so-called promissory notes – a mechanism devised to refinance Anglo using money from the Central Bank of Ireland but without breaching bank funding rules.
The latest instalment was due at the end of the month.
It is understood Dublin's plan was to replace the promissory note arrangement with a long-term government bond.
Finance Minister Michael Noonan is planning to address the Dail on the proposal tonight.
Ireland's total bank bailout cost about €64bn (£55bn).
The IBRC has been winding down the old loan books of Anglo for more than two years and at the same time attempting to recover debts.