It is understood the bank has seen presentations from Clemmow Hornby Inge and TBWA. No other agency is thought to be involved.
TBWA has struggled to manage the client conflict between The One Account and Abbey National, which it won from Euro RSCG Wnek Gosper in April.
The One Account managing director, Jayne-Anne Gadhia, is believed to have called the review.
The CHI founders Simon Clemmow and Johnny Hornby both worked on the account when they worked at TBWA. CHI is already on the RBS roster, having won the Avanta account at the end of last year.
In January, TBWA relaunched the business with a campaign that saw the revival of characters from the 70s children's TV show Hector's House.
The campaign was designed to rebrand it from Virgin One to The One Account.
RBS undertook the rebranding following its acquisition of the business from Virgin and AMP in July 2001. Under the terms of purchase, RBS only had permission to use the Virgin name until the end of last year.