The unit, 13.5 per cent owned by the bank, has been administered by the lender since it was created but has been in its non-core portfolio since 2008.
RBS has been running down the unit over the past five years, selling off chunks including Arrow Global, the debt collection agency if floated on the stock market earlier this year.
Its chief Lindsey McMurray is proposing the new deal, according to Sky News.
Under the arrangement RBS would still own 13.5 per cent of the unit and so benefit from its profits.
But it would no longer administer the unit in-house.
Instead McMurray and her team would set up a new company, potentially with a new name, and raise new funds to begin increasing the size of the fund once more and making new investments.
It is thought the arrangement could be included in new chief executive Ross McEwan’s wider review of the bailed-out bank.
He is accelerating the plans to run down the investment banking and overseas parts of the bank to focus on UK retail and commercial lending.
McEwan’s predecessor Stephen Hester had been praised for his role in turning RBS around, but was pushed out after clashing with the chancellor over how far and how fast the investment banking units should be cut back.
RBS declined to comment on the future of the Special Opportunities Fund.