The venture, which launched in April this year with £600m of funds to invest, is understood to have heard pitches from a small group of agencies within the past few weeks.
BSC's external comms are currently supported by HB Communications, which is believed to have repitched for the business against two larger corporate agencies.
The bank, initially called the Big Society Bank, was announced by the Government in July 2010, but was only formally launched earlier this year.
BSC is using £400m of funds from dormant UK accounts and £200m from the UK's big four banks to enable social ventures to access capital. BSC has so far invested £37m in eligible businesses and projects and is on target to invest £50m by the end of year and double that in 2013.
However, the organisation has faced criticism that it has failed to have the market impact initially hoped for, having only made a dozen investments from about 130 expressions of interest so far this year.
It is thought BSC is looking for its comms advisers to help it make more of an impact with the UK investment community and City media, and position the bank as a serious player in the UK financial landscape.
It is also understood the organisation recognises that its 'Big Society' moniker comes with some potentially negative political connotations and is looking to distance itself from the Government and reinforce its independence.
Alastair Ballantyne, head of comms at Big Society Capital, could not be reached for comment by the time PRWeek went to press.