Both sides denied recent reports that BA and Mr Branson were poised to drop litigation in an out-of-court settlement before the hearing.
British Airways is suing Virgin and Mr Branson over claims that BA used a dirty tricks campaign against its smaller rival. Virgin is suing BA for claiming that the allegations were a 'fabrication'.
However, there has been speculation that British Airways was prepared to drop its action and to pay Virgin damages and legal costs. Virgin's costs have been estimated at between pounds 400,000 and pounds 1m. A spokesman for BA declined to comment on reports of any climbdown.
He said: 'We will be in court on 11 January and the matter is in the hands of our lawyers.'
Virgin's spokesman said: 'We would not countenance an out-of- court settlement. Virgin will be in court on 11 January.'
A source close to the issue said, however, that a deal between the two sides had been virtually finalised and would be made public in court.
But even if an early settlement was reached in the UK, there is no guarantee that Virgin would not continue to air its alleged grievances elsewhere.
There has been speculation that the company might resort to the European Court of Justice or pursue the matter in the United States.Reuse content