Huge won the business after a pitch and is now expected to handle a revamp of the airline's flagship site.
BA called the review in September, with its marketing department handling the pitch directly.
The activity is separate to the larger digital review process that BA started a week after the BA.com pitch.
Oystercatchers is handling that process, which incorporates all of BA's digital advertising as well as social media activity.
Agencies on the longlist have been asked to respond with information by next week. Chemistry meetings will take place next month, with pitches expected to occur in January.
Being is the incumbent on BA's main digital account and has been invited to repitch for the business.
Earlier this year, BA launched its high-profile brand campaign, "To fly. To serve", to highlight the company's dedication to the aviation industry.
Created by Bartle Bogle Hegarty, the campaign included a 90-second TV ad that premiered on the airline's official Facebook page.