Last month, the BBC announced a shortlist of nine bidders for BBC Technology, a number that will be whittled down to three in April prior to the final contract being signed in September.
Because the deal is a wholesale sell-off, rather than an outsourcing contract, Tupe regulations, which protect employees' rights when a business is taken over, do not apply.
Broadcast union Bectu said industrial action was an option it would consider should job security for BBC Technology's 1,400 staff not be assured.
"Privatisation of BBC Technology has not been accepted by Bectu, and management have been warned of serious opposition to the plan," a union spokesman said. "Although the union is making no immediate threats of industrial action, there is a real possibility that this weapon could be used later in the discussions."
The BBC said there could have been up to 350 redundancies had BBC Technology been kept in-house.
The corporation said it was committed to protecting staff terms and conditions, even though Tupe rules would not apply, and would oblige the new owner to provide "broadly similar" pension entitlements.