The company, whose current brand spokesman is Sir Alan Sugar, is in the early stages of a review process, which will involve all of the company's existing agencies.
These are: EHS Brann, which handles direct marketing; OMD, which handles media planning; and Chick Smith Trott, which is responsible for TV ads.
Because it is government-backed, NS&I is forced to hold a statutory review of all of its accounts every five years.
The final date for a decision on its agency relationships is April 2008. The savings business has decided that it will need at least a year to make its decisions.
Following its most recent review, concluded in early 2003, the company re-appointed all of its existing agencies.
Its latest work has included Sugar attempting to convince the public to invest their money in premium bonds.
Garry Bond, the head of marketing services at NS&I, said: "The tenders for above- and below-the-line activity, and media planning, will be open to all who register an interest, as required by government purchasing rules. We would expect our existing agencies to be involved as well as any others who wish to submit proposals."