The group, which remains 81% owned by the taxpayer, has opened discussions with a number of private equity firms, the Sunday Times reported.
Private equity groups including CVC, KKR, Permira and Warburg Pincus are all said to be considering a proposal that would boost the balance sheet of the lender.
The Northern Irish lender has racked up big losses in recent years, largely due to poor quality loans originated before the financial crisis.
If any private equity cash boost did occur a merger with another Irish lender such as Danske Bank or Permanent TSB would be expected to follow.
RBS is currently unable to finance an overhaul of Ulster Bank but would likely see a considerable boost to the group’s share price if a private equity deal were to go ahead.