The British Business Bank is run by the Department for Business, Innovation and Skills and was first announced by Business Secretary Vince Cable in 2012.
A tender document seen by PRWeek states that the bank is looking for an agency to build awareness, with work building up to a state of the market report expected to launch around October.
The work is envisaged to last for six to nine months and the appointed agency will also be expected to build confidence among SMEs that finance markets "are changing for the better".
A British Business Bank spokesperson said: "We want to be seen as a catalyst to changing the structure of finance markets for smaller businesses, so they work more effectively and dynamically. As part of that, we see ourselves as champions for innovation and diversity in finance supply, enabling and promoting a greater choice of options and providers.
"We also want to be seen as a source of expertise and a trusted voice about finance for smaller businesses, so we can help build confidence in finance markets and the options available to smaller businesses."
The bank was created to bring together public and private sector funds with a particular focus on helping smaller companies prosper. At the time he announced it, Cable called it a "lasting monument" to the Government’s "determination to reshape finance" in the wake of the financial crash.
Target audiences will also include finance providers and intermediaries such as accountants and trade bodies.
The bank claims to have helped £782m reach smaller businesses in the last fiscal year with a range of initiatives including a start-up loans programme.