Blame Game
Tony Woodley, joint leader of Unite, said the current deal offered by BA chief executive Willie Walsh could not be accepted by his members.
He also said BA was wrong to blame Bassa, the Unite branch representing crew, for blocking the deal.
Unite members of BA cabin crew are set for a five-day strike on Monday.
It follows a series of walkouts in a long-running dispute over jobs, pay and working conditions.
BA and Unite are holding last-ditch talks to avert the latest round of industrial action later on Saturday, conciliation service Acas has confirmed.
But Mr Walsh, who has said the company will do everything it can to reach an agreement with Unite before Monday, has blamed Bassa for the failure to reach a deal.
BBC business correspondent Joe Lynam said the two sides were very close to reaching an agreement but there was still a big question over the issue of trust.
Chief Acas conciliator Peter Harwood expressed optimism about an agreement but warned that if a deal was not secured this weekend there was "every possibility that additional pressures on both sides will ensue which will make a final resolution more problematic".
Unite say the main stumbling blocks now are the travel perks that were taken away from members who went on strike in March and disciplinary action which has been taken against more than 50 of its members.
Bassa secretary Duncan Holley said he believed Mr Walsh was "determined to break the union".
Mr Holley, a former BA staffer who worked in cabin crews for 34 years until he was sacked this month after disciplinary hearings, told BBC Radio 4's Today programme that Mr Walsh had never agreed to negotiate with his 12,000 members.
"He keeps talking about us being dysfunctional - we actually are the biggest branch in the country; we represent a third of his workforce," he said.
He added that he did not want to disrupt customers' plans but he had to look after his 12,000 members.
The first strike is due to last for five days from Monday, but two more five-day stoppages are timetabled to begin on 30 May and 5 June.
BA plans to fly more than 60,000 customers a day next week, operating 60% of long-haul flights and 50% of short-haul services from Heathrow.
It says its services from Gatwick will be unaffected.
The airline is intending to lease up to eight aircraft with pilots and crew from other UK or European carriers.