Incumbent agencies include the Cheltenham-based TDA and Iceberg Marketing.
KLP Euro RSCG, the below-the-line division of Euro RSCG, has also worked for Abbey National on its card services marketing.
KLP's sister agency, Euro RSCG Wnek Gosper, recently lost the £27 million Abbey creative account to TBWA\ London. MindShare and Naked Communications replaced Carat on the media planning and buying business.
Abbey has spent £11 million on direct mail over the past year. In March, the last month for which figures are available, it mailed 3.5 million homes, according to Nielsen Media Research.
Arnold, who was installed as Abbey's chief executive last year, is spearheading an attempt by the bank to turn around its fortunes. It announced losses of close to £1 billion earlier this year and Arnold is attempting to create a more customer-focused business to address this.
In January, Abbey lost its head of customer communications, Jonathan Lathman, who left to run Sainsbury's direct marketing department. However, it recently hired the BT marketer, Angus Porter, in the more senior role of customer propositions director to lead its marketing effort.
Abbey is also expected to overhaul its brand after hiring Wolff Olins to develop a new identity. Reports suggested that Abbey National is to rebrand as The Abbey.