Military personnel are being asked to prepare to man Britain's borders when public sector workers stage a mass walkout next Wednesday, Sky sources have said.
It comes as Heathrow Airport bosses warned the strike on November 30 could cause "gridlock" as passengers are forced to remain on planes as queues build inside terminals.
Civil servants have also been approached to help out, with up to 18,000 immigration officials are expected to take part in the walkout.
Passengers travelling through Heathrow next week have been told they may have to queue for up to 12 hours during the strike.
And chiefs at airport operator BAA are even suggesting to airlines that they fly their planes half full.
The warning came in a letter to all airlines which fly to Heathrow from chief operating officer Normand Boivin.
He said BAA had "reluctantly concluded" that the UK Border Agency would be unable to provide a contingency plan to support normal operations.
Mr Boivin warned: "Modelling of the impacts of strike action on passenger flows at Heathrow show that there are likely to be very long delays of up to 12 hours to arriving passengers.
Alan Johnson MP backs the right to strike
Every independent trade union can ballot under very strict rules. If they can't do that over an issue as important as their pensions then what can they take industrial action over?
"The delays at immigration are likely to be so long that passengers could not be safely accommodated within the terminals and would need to be held on arriving aircraft.
"This, in turn, would quickly create gridlock at the airport with no available aircraft parking stands, mass cancellations for departing aircraft and diversions outside the UK for arriving aircraft," he told The Daily Telegraph.
British Airways say their customers will be able to switch their flights free of charge if they are concerned.
In a statement the airline said: "We understand there will be a significant risk of severe delays in passing through passport control, with potential knock-on effects on wider airport operations."
BA said it plans to run a normal schedule and is doing everything it can to protect customers.
The UK Border Agency has asked staff working in embassies and high commissions in South Africa, India and Russia to return to Britain to help with cover for their striking colleagues.
In a statement UKBA said securing the border was its priority.
Passengers may face a longer wait at Heathrow Airport
Ministers have condemned the planned strike over public sector pensions which could see two million workers stay away from work.
But the TUC said the Government's estimate that the strike could cost the UK £500m in lost revenue was "fantasy economics".
Striking workers have been given support from former Labour home secretary Alan Johnson, who joined a union when he worked as a postman and went on to take full-time union posts.
"Every independent trade union can ballot under very strict rules. If they can't do that over an issue as important as their pensions then what can they take industrial action over?" he told the BBC.
"On this issue, I think the Government generally want to negotiate a settlement but they started off badly."
However, Labour leader Ed Miliband has called instead for compromise between the Government and union leaders.
"I am very concerned about the cost of these strikes and that is why both sides must work to stop these strikes happening," he said.