British Gas is proposing to cut 684 office-based jobs and close an office in Oldbury under plans to "consolidate" its operations.
The company said it will consult workers and unions over the next 45 days and will "explore redeployment opportunities" for staff if the West Midlands closure is confirmed.
Claire Miles, managing director of customer operations, said: "Since last summer British Gas has been implementing a strategy to improve service and reduce costs, to ensure we can price competitively. We must also respond to the changing needs of our customers, and they increasingly want to contact us online.
"For these reasons we are planning to consolidate our activity on fewer sites, and we have made the difficult decision to propose closing our Oldbury office and call centre.
"I recognise that today's announcement represents difficult news for our employees who may be affected. Our priority now is to support all those potentially impacted, and to ensure a fair and transparent consultation process, working with our people and their representatives."
Brian Strutton, national officer of the GMB union, said: "This announcement has come completely out of the blue and is further evidence of the way British Gas now sees staff as pawns to be sacrificed when it suits.
"The Oldbury office has been performing well, the staff there have been delivering everything asked of them and more, yet all the while the company's top brass on their multimillion-pound pay packages have been harbouring secret plans to shut them down.
"The news will be devastating for the workforce and the local community, coming hot on the heels of npower's decision to also cut back its operations in Oldbury.
"GMB will fight British Gas to try to protect every job we can but today things look bleak for the Oldbury workers."
The Unison union's national energy officer, Matt Lay, said: "This is terrible news for the company's Birmingham-based employees, who will be devastated at the prospect of losing their jobs. British Gas might be losing customers, but it's still a very profitable business.
"The scale of the cuts will make compulsory redundancies hard to avoid. We'll now be working closely with British Gas to make sure that all workers affected are given as much help as possible to find new jobs, either within the company or with other employers in the area."
David Cameron said the Government stood ready to help those affected by the closure.
"We will make sure that a taskforce of ministers is available to talk to the company, to talk to the local community, to provide all the assistance in terms of re-training and other things that can be done to help," he told MPs at Prime Minister's Questions.