Talks between the union and British Airways management concluded on Wednesday “to the satisfaction of both parties”. The unions will consider the latest offer on Thursday.
The offer could provide an end to the 18-month dispute which has cost the airline more than 150 million pounds.
Unite, which represents the majority of BA crew, said general secretary Len McCluskey would brief members today about progress made in talks with BA management.
A member of British Airlines Stewards and Stewardesses Association (BASSA) said union members would be asked to endorse the settlement at the meeting and would then be formally balloted within weeks.
Unite would not comment on the status of talks, while BA said the talks were continuing.
BA cabin crew staged 22 days of strikes last year, causing misery for travellers and huge losses to the airline.
While the two sides, which came close to a deal last year, had failed to reach an agreement in talks spanning 18 months, recent changes in leadership at Unite and BA gave fresh impetus to moves to reach a settlement.
BA’s former chief executive, Willie Walsh, became boss of International Airlines Group – formed by the merger of BA and Iberia earlier this year – and was succeeded by Keith Williams.
Unite elected McCluskey, seen as one of Britain’s more militant union leaders, to succeed former joint general secretaries Tony Woodley and Derek Simpson.
The dispute started in November 2009 when BA cut the number of crew on some long-haul flights to 14 from 15 and introduced a two-year pay freeze from 2010.
Travel perks were taken away from about 7,000 cabin crew who took part in the original strikes, and the row became one of the most bitter disputes in Britain’s recent industrial history.