The review is believed to be in its early stages and focused on the bank’s UK retail and commercial operations.
Quiller landed the account in a competitive pitch in 2009, when it was thought to be worth £150,000 annually.
The account had been with Burson-Marsteller, which did not repitch, for less than a year, after seven years with Bell Pottinger Public Affairs.
HSBC uses FleishmanHillard for its European public affairs work and paid the agency between €200,000 and €250,000 in 2013, according to the EU Transparency Register.
Its UK public affairs monitoring is handled by Cicero Communications.
A HSBC spokesman said: "HSBC, in keeping with its policy of ensuring the periodic review all supplier arrangements, is currently conducting a review of public affairs consultancy support for its UK Public Policy team.
"Invitations to participate were issued in the first week of June, the deadline for expressions of interest has now passed, and the review is expected to conclude by the end of August."
Quiller and Cicero were unavailable for comment.
This story was amended at 1pm on 24 June to include comment from HSBC.