The TUC, which is chairing the meetings, has set the deadline for the “close of play” on Tuesday 9 March.
In February, BA crew members voted in favour of strike action over pay and working conditions.
The Unite union must give a week’s notice about any strike action, and has said that its members will not strike over the Easter period.
Should talks end without a resolution and the union decide to name strike dates immediately, industrial action could begin as early as Tuesday 16 March.