RBS said last night it was seeking to sell up to 300 million Direct Line shares, accounting for 20% of the group. This would leave it sitting on 427.4 million shares, a 28.5% stake.
European competition officials have told RBS to sell Direct Line by the end of 2014 as a condition of approving its 2008 Government bail-out.
RBS previously sold stakes when it floated Direct Line last October and in a sale in March.
The bank is expected to ask for an extension to the deadline of the end of this year to sell the 315 branches in its Rainbow portfolio, which are also part of the European Commission deal.