RBS was bailed out by the government in 2008 at the onset of the financial crisis and is now 83% owned by taxpayers.
The insurance business has been looking to develop distinct propositions for its main brands before it is offloaded.
It recently appointed former British Gas commercial chief Rick Vlemmiks to the role of chief marketing officer to oversee marketing strategy for its UK brand portfolio, which also includes Green Flag and Privilege.
A spokeswoman for RBS Insurance declined to comment. The rebrand is expected to be unveiled next week.