The Troika wants banks to conclude agreements with one quarter of borrowers in arrears by the end of March next year, RTÉ News has learned.
Banks have already been set targets to make offers to distressed borrowers by the Central Bank.
However, observers say the goal of finalising arrangements with 25% of distressed borrowers will be very onerous for Irish banks.
This means banks must either modify loans so customers can meet new lower repayments or enter resolution agreements, which means customers will have to sell homes by trading down or in some cases face repossession.
Last week AIB, Bank of Ireland, Permanent TSB and Ulster Bank told the Oireachtas finance committee they would meet the target of making offers to borrowers.
The banks were criticised because almost 15,000 of offers were in the form of letters threatening legal action.
The more demanding target for the banks to meet will be to conclude agreements with 15% of borrowers in arrears by the end of this year.
It is understood the targets for concluding deals will escalate next year to the point where the banks will have to have finalised arrangements with the majority of those in arrears by the end of 2014.
RTÉ News understands discussions are continuing with the Troika on the issue at present.
The Department of Finance declined to comment.