In October, RBS was told by the FCA it must pay an amount that would be a record for IT failures. In 2012, 7m customers were locked out of their accounts for almost a month.
The cause of the IT problem was a failed software upgrade that left account holders unable to transfer funds into or out of their accounts.
Sky News reports that RBS could receive a discount of up to 30 per cent on the proposed fine if it settles within the 28-day window given by the FCA. The City watchdog began investigating the error in April last year.
Last week, RBS set aside £400m to cover the potential costs from an investigation into the alleged foreign exchange manipulation.
In October, UK Financial Investments' executives told MPs the bailed-out bank was close to being ready for privatisation but the threat of serious fines is holding back a major share sale. The taxpayer still owns 81 per cent of RBS.