CityAM said that banks have been placed on high alert as government ministers kick off a process to reduce the taxpayer's 70.5% stake in RBS.
The newspaper said precise details on the sell-off remain unclear but bankers said it was paramount the government is able to demonstrate it is getting value for money for the sale.
Sky News reported that a disposal could target proceeds of more than £3bn by selling around 10% of RBS.
RBS was rescued by UK taxpayers in a £45bn package during the financial crisis of 2008.
Earlier this month, RBS agreed to pay US$4.9bn (£3.7bn) to resolve a US Department of Justice probe into the sale of mortgage-backed securities ahead of the 2008 financial crisis.
That smaller than expected settlement came after the lender posted its first annual profit in almost a decade in 2017 and looks to have cleared the way for RBS to resume dividend payments.
RBS holds its annual general meeting on Wednesday.
In early morning trading, RBS shares were down 3.2% at 280.4p.
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