Ulster Bank already cut 1,000 jobs in 2009 - 14% of its workforce
The report, published by US financial news provider Bloomberg, is reported to be sourced from “two people with knowledge of the plan”.
No job numbers have been reported by
The news comes as the chairman of UK Financial Investments, which is managing the taxpayer states in both RBS and Lloyds Banking Group announced he is to retire.
Sir David Cooksey also warned disposal of the UK Government's stakes in both banks could take "longer than expected".
RBS is reported to be looking to cut costs at the Dublin-based bank by as much as Euro 50 million (£41.2 million).
Around 1,000 jobs, or 14 per cent of Ulster Bank's workforce, were cut in 2009, and an announcement is expected on Thursday with regards to further job cuts.
RBS pumped about Euro 2.7 billion (£2.23 billion) of capital into Ulster Bank up to the end of 2009, according to records in Dublin's Company Registration Office.
However, Bloomberg's sources suggest this latest cost saving drive will not come solely from job cuts.
RBS is also expected to announce the closure of large parts of its investment arm, Global Banking and Markets, which could see as many as 5,000 jobs axed.
The Edinburgh-based bank has so far failed to find a buyer for the investment banking operations it has up for sale, despite reports earlier this week the bank was considering incentivising the deal by way of a multi-million pound dowry payment to any potential buyer.
Meanwhile the chairman of UK Financial Investments, (UKFI) responsible for managing the UK Government's shareholdings in RBS and Lloyds Banking Group, has announced he is to retire.
Sir David Cooksey will be replaced by chief executive Robin Budenberg when he steps down in April.
The reshuffle comes as the government looks set to remain a significant shareholder in RBS, in which it has an 83 per cent stake, and Lloyds, in which it has a 41 per cent holding, for some time in the light of plunging equity markets and an uncertain economy.
Cooksey said: "Now is the right time for me to hand over the reins.
“The last two and a half years have been extremely challenging for UKFI and for the banks in which it has investments.”
He added: "Disposal of the investments in Lloyds and RBS will inevitably take longer than originally expected, given the challenging economic and banking industry environments both in the UK and globally."
Jim O'Neil, currently responsible for the RBS and Lloyds investments, will replace Budenberg as chief executive on April 2.