London Underground (LU) staff have been offered a bonus of £850 each to work during this summer's Olympics.
The Rail, Maritime and Transport (RMT) union said it would consider the offer made by LU, which would benefit 18,000 workers.
LU said in return for the payment it was asking staff to work longer shifts at different times of the day and to be prepared to work extra hours.
Train firms are to pay workers between £500 and £2,500 during the Games.
LU made the new offer to the RMT during talks at the conciliation service Acas.
The union had previously rejected an offer of £100 bonus calling it "derisory".
Ballot over leave
RMT General Secretary Bob Crow said: "Clearly moving from offering nothing to the latest offer of £850 is a massive shift on the part of LU.
"The offer will now be considered by our reps and by the full executive before we make a formal response."
But the union has said it will ballot administrative staff at Transport for London (TfL) for industrial action over "severely restricted" annual leave during the Games.
It also plans to ballot workers at Tube Lines, now a subsidiary of TfL, calling for them to be be eligible for pensions and travel concessions from TfL.
Howard Collins, LU's chief operating officer, said: "We have put forward an offer which would see station, maintenance, service control staff and operational managers receive up to £850 for working flexibly during the 2012 London Games, subject to attendance, customer satisfaction scores and agreement from operational staff to work flexibly in order to deliver a successful Games.
"In return we are asking staff to work longer hours at different times of the day, to be prepared to work extra hours and to be more flexible in how and where they carry our their role for us during these crucial weeks."