The members of the Unite union are striking in protest at changes to working conditions introduced by the airline in November, including a pay freeze and a reduction in the number of crew on long-haul flights.
However, the union confirmed British Airways has made a new offer, which it will put to a member ballot by the middle of next week. If members vote in favour of accepting the terms, the strike will be called off.
Unite said, should no resolution be reached after the strike has taken place, further industrial action will be called after 14 April.
The union members had originally voted in favour of a strike over Christmas last year, but it was blocked by the high court after it emerged that about 900 cabin crew were balloted, despite having taken voluntary redundancy.
It marks another blow for the embattled airline, which has also come under recent pressure from rivals over its merger with American Airlines.
As revealed in Marketing last week (2 March), British Airways asked digital agency Agency.com to create a social media strategy aimed at providing customers with the latest information on services, should the industrial action go ahead.
Budget carrier easyJet has announced that British Airways Gold Card holders will be entitled to free access to Speedy Boarding on easyJet flights, for every day the strike is taking place.