IAG also owns Spanish airline Iberia and Ireland's Aer Lingus.
In a statement, IAG said: "The proposals remain subject to consultation, but it is likely that they will affect most of British Airways' employees and may result in the redundancy of up to 12,000 of them."
The company said it will take several years for air travel to return to pre-virus levels, a warning that has been echoed by airlines across the world.
Alongside IAG's statement, BA chief executive Alex Cruz wrote in a letter to staff: "In the last few weeks, the outlook for the aviation industry has worsened further and we must take action now. We are a strong, well-managed business that has faced into, and overcome, many crises in our hundred-year history.
"We must overcome this crisis ourselves, too. There is no government bailout standing by for BA and we cannot expect the taxpayer to offset salaries indefinitely... We will see some airlines go out of business."
About 4,500 pilots and 16,000 cabin crew work for BA, which has already put almost 23,000 staff on furlough.
Balpa's general secretary Brian Strutton said: "This has come as a bolt out of the blue from an airline that said it was wealthy enough to weather the Covid storm and declined any government support.
"Balpa does not accept that a case has been made for these job losses and we will be fighting to save every single one."
Airlines across the world have warned they face a fight for survival.
Lufthansa, the German airline group, is considering filing for creditor protection, according to its cabin crew union.
Norwegian Air Shuttle warned this week that the bulk of its fleet is likely to remain grounded for the next 12 months. The company warned that a full recovery would not take place until 2022, laying bare the scale of the crisis engulfing the industry.
