According to Reuters, British Airways said on Tuesday it had begun a 90-day consultation with union Unite and believed that it would be able to make the reductions through voluntary redundancies.
Unite officer Oliver Richardson said the union would be working to ensure that BA "keeps its promise of 'no compulsory' redundancies".
"Any attempts to force people wanting to continue working for BA out of a job will be resisted," he said.
BA fought a protracted battle over pay and staffing in 2010 and 2011 with cabin crew, which was resolved last year after a number of disruptive strikes.
Its partner airline Iberia said earlier this month it would axe about 4,500 jobs as it cut capacity to make it more competitive. A series of strikes are planned next month in protest.