The source also revealed that the company's new chief executive, Charles Woodburn, could be "trimming" the firm's workforce across other locations.
Sky reported that the cuts are understood to relate largely to the sluggish pace of production of the Eurofighter Typhoon fighter aircraft, and uncertainty around the timing of a potentially large order from Saudi Arabia.
The Typhoon's participation in any future European fighter programme is in doubt, after France and Germany announced plans in July to jointly develop a new European fighter jet - a move that was widely seen as a snub to the United Kingdom due to Brexit.
The company is expected to make the announcement on Tuesday, with "well over 1,000" jobs expected to be cut.
BAE employs 34,600 people in the United Kingdom, accounting for almost half of its 83,100 global workforce.
"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", the firm said in a brief statement issued to media.
Theresa May's official spokesperson said that it is wrong to pre-empt the severity of these jobs cuts, adding: "We do have a long track record of working with BAE systems and with its works and we'll continue to do so".
"We obviously have to review our (Typhoon) production demand very carefully", Mr Woodburn said in August.