Labour described the news as “devastating”, while unions were seeking information, having been braced for cuts because of a lack of future work.
The announcement, expected in the next few days, is likely to mainly affect sites at Warton and Samlesbury in Lancashire, where aircraft assembly takes place.
A BAE Systems spokesman said: “BAE Systems continually reviews its operations to make sure we are performing as effectively and efficiently as possible, delivering our commitments to existing customers and ensuring we are best placed to secure future business.
“If and when there are any changes proposed we are committed to communicating with our employees and their representatives first.”
Nia Griffith, shadow defence secretary, said: “This is devastating news for the workers and their families.
“The men and women who work on the Eurofighter are highly skilled and the potential loss of these jobs would have an appalling impact on them, the local economy and wider supply chains.
“The Government must come forward urgently with a clear plan to secure these jobs at BAE, as well as a proper defence industrial strategy to give the industry the certainty that it needs.”
The Prime Minister’s official spokesman told a Westminster media briefing: “No announcement has been made from the company, so I think it would be wrong for me to pre-empt any announcement.
“What I would say is we do have a long track record of working with BAE Systems and its workers and we will continue to do so.”