Italian news agencies initially reported CAI had withdrawn its offer, but then said there was no confirmation that step has yet been formally taken.
Ahead of the meeting, Maurizio Sacconi, Italy's labour minister, said Alitalia faced a "very real risk" of liquidation if CAI and the unions could not reach a last-minute decision.
"I really think the future of Alitalia is hanging by a thread," he said.
With Alitalia in special administration and running out of cash to buy fuel, the risk that the airline had only days or hours of life left seemed more palpable than ever.
"There is no room for negotiations left ... liquidation is a very real risk," Sacconi said.