BA is still pushing ahead with anto prevent the walkout, which is scheduled to start Monday.
The planned strike, which escalates a bitter dispute over job cuts, pay and working conditions, threatens to ruin travel plans for a million passengers and cost the loss-making airline tens of million pounds (dollars) each day.
Unite union general secretary Tony Woodley said the union was prepared to call off the strike - but only if BA agreed to suspend its imposition of the new conditions on cabin crew.
"Let's have a pause for peace, and we will call the strike off," Woodley told BBC television.
Woodley said that BA, which argues the changes to staffing and pay are necessary to ride out its dire financial situation, had already declined a similar offer at talks Friday.
The meeting between BA management and Unite leaders is due to take place at 3 p.m. (10 a.m. EST) - after a scheduled 2 p.m. High Court hearing on the injunction. The airline has lodged its claim on the basis the strike ballot was invalid because it included votes from people no longer employed by the airline.
The planned strike couldn't come at a worse time for BA, which has been one of the airlines worst hit by the global recession because of its heavy running costs and reliance on increasingly unpopular premium fares.
Already expected to post record losses this year, analysts estimate the airline will lose up to 30 million pounds ($49 million) a day if the strike goes ahead during a time when it normally operates 650 flights and carries 90,000 passengers daily.
Rival travel companies have been quick to take advantage. Among them, Virgin Atlantic - a strong critic of BA's proposed revenue-sharing deal with American Airlines - has said it will employ larger aircraft on key routes out of London, including to New York, Washington and Delhi, over the planned strike period.
But angry passengers still face soaring prices for alternative flights - or train journeys - to enjoy Christmas and New Year celebrations at the end of what for many has been a tough year financially.
British Prime Minister Gordon Brown waded into the increasingly acrimonious dispute on Wednesday, urging BA and Unite to come to a deal to ensure travelers "a strike-free and trouble-free Christmas."
Brown said he discussed the issue with Transport Minister Andrew Adonis early Wednesday and the government was eager to bring the two sides together.
"We are agreed that the different sides in this dispute have got to look outwards and not inwards, they have got to think of the passengers that they serve, they have got to think about the future of their company," Brown told Britain's GMTV from Copenhagen, where he is attending the summit on climate change.
The union alleges the changes to pay and conditions are in breach of contract, but last month agreed to fly with reduced staffing after failing to win its own court injunction banning their imposition until a High Court decision on the dispute Feb. 1.