Centrica, who own British Gas, confirmed on Thursday, April 4 that they are planning to close the Canal Street offices and that have been informed.
They are yet to announce whether there will be any job losses but have confirmed a total of 500 are at risk across the UK.
Staff will be moved to their office at New Bridge House in Holbeck.
A spokesperson confirmed that the move is to 'consolidate' the twoLeeds sites into one location.
The ageing infrastructure of the Canal Street office has been cited as a reason.
In a statement released today, Centrica said: "Centrica has proposed a number of changes across the UK to its employees today, which include role reductions to reduce management layers, role reduction to reduce back office functions to improve efficiency, the future consolidation of its two offices in Leeds, and two in Glasgow.
"Around 400 jobs in Scotland are at risk, from a total of around 500 around the UK.
"Over the next 45 days, as part of a full consultation process, the company will discuss the proposals and seek the views of employees and their representatives."
Sarwjit Sambhi, CEO Centrica Consumer, said: “This difficult decision was made because we need to respond to the growing challenges we face. Our customers want more from us. Competition is fierce and we're operating under a price cap."
Unions UNISON and GMB have commented on the announcement of 500 redundancies at British Gas.
UNISON national energy officer Matt Lay said: “Any loss of jobs is disappointing and staff will understandably feel anxious.
“We’ll be working closely with British Gas to ensure no compulsory redundancies and affected employees will be able to move to other local sites, receive training to take on new roles or take advantage of the voluntary severance scheme.
“UNISON and the GMB have been liaising with the company to minimise the impact of the job losses. So it’s disappointing that some staff found out about the story from comments made to the media, adding to their distress.
“Energy firms in the UK are operating under challenging circumstances made worse by the market instability that a government all-consumed by Brexit seems intent on ignoring.”
Justin Bowden, GMB National Secretary, said: “GMB is confident that the vast majority of staff affected by these closures can be redeployed within British Gas and we will do everything in our power to ensure that every GMB member who wants to stay with the company has a job.”