The brief, which is with The Haystack Group, involves the creation of a brand identity similar to Direct Line's red telephone or Churchill Insurance's talking dog.
St Luke's, HHCL/Red Cell, McCann Erickson Manchester, Walsh Trott Chick Smith and WCRS presented creative ideas for the business on Tuesday. A shortlist of four will pitch next Monday.
Abbott Mead Vickers BBDO, the incumbent on Sainsbury's Bank as well as on the retailer's main account, is not involved in the pitch, which is being turned around quickly for a launch in October.
Sainsbury's Bank is a joint venture between the supermarket and HBOS.
HBOS also owns eSure in conjunction with the Direct Line founder, Peter Wood.
Last month, Campaign revealed that Sainsbury's had awarded a slice of its above-the-line print advertising to its contract publishing agency, New Crane.
While Sainsbury's played down its significance, the news fuelled speculation that the relationship between Sainsbury's and AMV is under strain.
The supermarket's Jamie Oliver commercials have been attacked for becoming tired recently. However, Oliver signed a new two-year contract in May.
Any decision to change strategy will be led by Stephen Nelson, who became the retailer's marketing director in June.
Sainsbury's is also under intense pressure to improve its financial performance and is seen as a vulnerable takeover target.