HPM deputy CEO Charles Metcalfe confirmed he had shortlisted four agencies for the account after an initial line-up of six.
The account is worth £5,000 a month and HPM plans to appoint a new agency in May.
Metcalfe added that HPM’s review was a result of what he described as ‘good healthy business practice’.
The review does not affect Redwood Consulting, which HPM retains for PR on its property investments.
The successful agency will handle media relations and corporate profiling of HPM, which manages around £45bn of company pension funds. The company’s most high-profile client is the BT Pension Scheme (BTPS), which set up Hermes to manage its £26bn fund.
Much of the account will be project-based and concerned with advising HPM on the PR issues surrounding shareholder engagement and corporate governance. As a major fund manager, the firm has a high profile as a shareholder in some of the UK’s largest companies.
Last month, HPM announced it would be investing around £500m in hedge funds over the next 18 months on behalf of BTPS. The investment is believed to be the largest allocation of funds to hedging strategies by a UK institutional investor.