A spokesman for Virgin said: 'If we reach a successful settlement next week we will not take action in the US. But otherwise we will, in the next week or two.' The deadline had been set for last Friday evening.
He said the company was furious that proposals for a settlement leaked out over the weekend. Both sides had agreed not to comment until the end of their talks.
Mr Branson is seeking financial compensation from BA for 'serious commercial damage' done by the dirty tricks affair, as well as the transfer of some BA slots at Heathrow to Virgin and a written undertaking by BA not to repeat its behaviour.
It is understood that during last week BA offered a three-part plan including a pounds 3m payment to cover earlier maintenance delays. Virgin says that its claim is for pounds 6m and that this issue is unconnected to the present dispute.
BA offered to go to arbitration over passenger poaching, but Virgin has rejected this suggestion as unacceptable.
BA also offered to use its influence with the Civil Aviation Authority to help Virgin expand international routes.
A Virgin spokesman said: 'It (the leak) was certainly not from us. We are furious about it.' It is understood that BA was also angry that information about an exchange of letters had emerged before negotiations were complete.
The row is expected to overshadow British Airways' results, due tomorrow. On the day of his appointment as chairman, on the sudden resignation of Lord King, Sir Colin Marshall warned that business had slowed.
BA has new planes starting flying in the spring, as part of its expansion plans. Sir Colin expected business to pick up by the time additional planes arrive.