The briefs with the French Energy giant, which is planning to build a host of new nuclear power plants in the UK, are understood to be worth several hundred thousand pounds a year.
MHP - formed by the merger of Mandate, Hogarth and Penrose Financial - has held the PA account for three years.
It is thought that both Brunswick and MHP intend to re-pitch for their respective accounts.
The successful agencies will report Kaa Holmes, head of corporate media relations, and Victoria MacGregor, head of PA, who in turn both report tot EDF's director of comms Andrew Brown.
EDF said in a statement to PRWeek that the review was part of its 'normal procurement processes'.
The statement read: 'EDF Energy's corporate public relations and public affairs activities form an important part of the company's commitment to openness and to excellence in comms with stakeholders.'
A key aspect of the work is thought to be supporting the firm's nuclear ambitions and influencing media and political opinions of the nuclear industry.
EDF already operates 58 nuclear reactors in France and has become the leading corporate voice in the British nuclear industry after its purchase of British Energy in September 2008.
The firm is in dialogue with the Government over a new nuclear reactor at Hinkley Point in Somerset. Local opinion on the is sharply divided, although EDF points to an ICM survey it commissioned that found 85 per cent support for the plant.
Brunswick's brief centres on corporate PR rather than financial comms, given the firm does not have a UK listing. The City agency led comms on EDF's purchase of British Energy.
In July the firm sold its UK networks business for £5.8bn to concentrate on power generation and supply.
EDF handed Weber Shandwick a £500,000 contract in March to support its customer comms.