The board of the Edinburgh-based institution is thought to be considering the futures of one or more key staff, with a decision from UK and US authorities imminent. John Hourican, head of its investment bank, and head of markets Peter Nielsen are reportedly the most vulnerable.
It is understood that if one or other of these executives is asked to leave, it will be because the board has concluded they should have been aware of what was going on.
Neither man was directly involved in the rigging of Libor [the London Interbank Offered Rate] and other important rates.
The scandal has already claimed the scalps of several senior banking figures, including Barclays chief executive Bob Diamond.
RBS, which is 82% owned by the taxpayer, is expecting a fine significantly higher than the $450 million (£290m) slapped on Barclays in June.
Speculation has suggested it could be in the region of £350m. Swiss-based UBS was fined $1.5 billion (£940m) for its part in the scandal.
As chief executive of markets and international banking, Mr Hourican was paid a £751,000 salary and a £2.5m bonus last year. Earlier this year he cashed in share awards worth more than £4m. He has worked for RBS since 1997 and still has several million RBS shares and options.
A source said: "The board will want to make sure serious consideration is given to proper accountability."
Last year Barclays chief operating officer Jerry del Missier was one of four directors to depart in the wake of the Libor scandal. He admitted he told traders to lower the bank's Libor submissions in the autumn of 2008.
However, the position of RBS chief executive Stephen Hester is unaffected because he did not work at RBS when the fixing was taking place.
The bank has parted company with a number of the traders involved. It is expected it will cut bonuses for last year paid to its investment bankers as a result of the scandal.
RBS said: "Discussions with various authorities in relation to Libor-setting are ongoing."
At least 16 institutions across the world are under investigation over Libor.