Marshall Aerospace and Defence Group, based at Cambridge Airport, is considering relocating to Cranfield.
And if the move goes ahead, 2,000 engineering jobs could be created in the area.
A Central Bedfordshire Council spokesman said: “This is an exciting opportunity and one which we welcome.
“Marshall Aerospace and Defence Group is a long-established business and a large employer.
“We will be working with partners to see how we can support them and Cranfield University.”
The firm is planning to build 12,000 homes and five million sq ft of business premises at Cambridge Airport and move by 2030.
A spokesman said the company needed to invest in new facilities, and “the relocation, coupled with the development of our land in Cambridge, will provide us with an extraordinary opportunity to achieve this”.
Other sites under consideration are Duxford and Wyton in Cambridgeshire.
However, the plans have come under fire from trade unionists.
The Unite union, which has 900 members at the Marshall Aerospace and Defence Group, wants urgent talks.
Regional officer Roger Dillon said: “We are talking about highly-skilled engineering jobs that are part of the lifeblood of the vibrant Cambridge economy.”
“Unite is very disappointed that we were not involved in the discussions prior to the announcement.”