The bank has been a flagship account of Weber Shandwick’s public affairs division – led by Jon McLeod – for around a decade.
The pitch, which will happen over the next few weeks, takes place amid a fractious political environment for UK bankers after the row over RBS chief Stephen Hester’s bonus.
A spokeswoman confirmed that the pitch is underway and that Weber Shandwick would repitch for the account.
Cicero, which currently works for the bank's investment banking business Barclays Capital, is also understood to be involved in the pitch for the main PA account.
Agencies were asked for written submissions at the end of last month.
Last November, Barclays pitched out its PR support for its £500,000 small business competition One Small Step.