It is understood that National Grid has asked a number of agencies for written submissions and will hold face-to-face meetings with shortlisted agencies during the coming weeks.
Brunswick has held the account since 2007, when it picked it up from Citigate Dewe Rogerson.
It is thought that financial PR heavyweights including Finsbury, FTI Consulting and Tulchan Communications are in contention.
National Grid and Brunswick did not respond to requests for comment.
It is thought the brief encompasses financial comms and corporate positioning, and will take effect in the New Year.
National Grid owns and runs the UK's electricity network and has also operated the gas transmission network since its merger with Transco in 2002.
A key issue for the successful agency will be supporting the firm's comms through energy regulator Ofgem's review of electricity and gas network pricing. The review will set price controls for eight years and are designed to provide stronger incentives for networks to manage costs.
More generally, the Government is pushing for a 'greening' of the UK energy supply in a bid to lower carbon emissions and increase energy from alternative sources.
The national grid will need to upgrade its infrastructure to cope with the electricity that the wind energy industry aims to produce. There are likely to be a number of comms issues around the upgrade and need for new overhead cabling and pylons across the country.
A City PR source added that relations with the investor community may need smoothing after the company launched a rights issue last year to a mixed response.