The ASTI has confirmed its central executive committee will meet again next Saturday to consider developments in its 30% pay claim.
However, it is unclear if a Labour Court recommendation on the claim will be drawn up in time.
The court has spent the past few weeks considering a number of other disputes, including the Aer Lingus cabin crew row.
This means it will only begin to deal with the ASTI claim next week, leaving just five days for the industrial relations body to consider the issue and make a recommendation.
Some members of the ASTI have warned that if no concrete proposals are ready by next weekend, they will demand the re-imposition of industrial action.