The account is currently handled by The Gate, which won it as Chick Smith Trott in 2007.
All agencies on the CCS creative roster were invited to participate in the process. They include Abbott Mead Vickers BBDO, DLKW Lowe, Engine, Enter, Inferno, Kindred, M&C Saatchi, McCann London, Ogilvy Group and Rainey Kelly Campbell Roalfe/Y&R.
Lord Sugar has been a frontman for NS&I ads but, under civil-service rules, was forced to step down in 2009 when he became an advisor to the then prime minister Gordon Brown.
Other personalities to have featured in ads include Sir Bob Geldof, Stephen Hawking and Germaine Greer.
NS&I is best known for its premium bonds but also offers other savings and investments. It has more than 25 million customers.
Last week, HM Treasury launched an ad campaign, created by Ogilvy & Mather, to support its help-to-buy scheme after hiring the WPP agency at the end of last year.