In addition to owning British Gas, the FTSE 100 constituent has interests in oil and gas exploration and production, power generation and trading.
It is set to hold pitches later this month, but Finsbury is understood to have declined an invitation to take part.
The review of the group’s only retained agency account comes as the big six energy companies battle public and political pressure and after Centrica posted a profit warning this winter.
It also follows the departure in December of chairman Sir Roger Carr, who is thought to be close to Finsbury founder Roland Rudd.
As well as corporate and City work, the brief – estimated by one agency figure to be worth a high six-figure sum – is also likely to include an element of public affairs, though public affairs-specific agencies are not being sought.
In a further change Nick Baird, a former UK Trade & Investment CEO, is arriving at Centrica in March as group corporate comms director to help lead on strategy.
A Centrica spokeswoman said: "We are looking for a PR agency with a strong integrated offer to support us at group level focusing on financial and corporate communications. The successful agency will be one that demonstrates a good understanding of our business and the political and regulatory market we operate in."
Centrica was at the heart of the debate that followed Labour’s promise to freeze energy prices in the autumn, taking a more aggressive stance than some of its rivals.
The group – which made a profit of £1.4bn after tax in 2012 – implied that it would either go bust or leave the UK if the plan was put into action, while Carr warned the move could cause "economic ruin" for the country.
Issuing a profit warning in November, it said it had to increase energy bills 9.2 per cent this winter to offset losses but added that it would pass on any savings from government relief of green levies to households, while CEO Sam Laidlaw waived his bonus.