The move would cut the value of his pension pot by around £4m but he would still be left with £350,000 a year.
The report says Goodwin offered take a reduced pension after RBS threatened him with legal action.
The bank is likely to accept Sir Fred Goodwin’s offer but the BBC says the Government, which owns 70 per cent of RBS, may reject the deal on the basis that it would still leave Sir Fred with a bigger pension than he would have received if he had been fired instead of leaving on agreed terms.
RBS agreed in October 2008 that Sir Fred would be allowed to take his full £703,000 a year pension at age 50, rather than having to take a reduced rate for claiming it early.
RBS almost collapsed while Sir Fred was at the helm. He has been critisised for pushing through RBS’ acquisition of ABN Amro, which lumbered the bank with significant levels of debt.