The bank currently splits its creative business between Saatchi & Saatchi, Creative Juice-SIL and SM Media,
Its media business is handled by KHK Advertising, which has been invited to repitch for the account.
A decision on the appointments will be made before Christmas, with the successful agencies starting work on the accounts in January next year.
Last year, RHB launched a $2 million corporate branding campaign that aimed to inform Malaysians of the merging of the brand's four core business units.