Tiger Airways Australia is more likely than not to be back in the air next week, after a court hearing into an extension of its flying ban was postponed for the fourth time this morning.

Tiger Airways, which had its licence to fly suspended by the Civil Aviation Safety Authority on July 1, has applied to the Federal Court in Melbourne to shift the hearing to 4 p.m. on Friday.

In the meantime, the airline continues to furnish its responses to the safety regulator on how it will be able to meet strict new safety conditions imposed on the airline's licence to fly. The Civil Aviation Safety Authority's (CASA) investigators are continuing to assess and verify the robustness of the airline's responses.

Friday's 4 p.m. hearing is an indication, sources close to the talks suggest, that Tiger hopes to be able to satisfy the safety regulator's conditions by the end of the working week.

If that's the case, and the safety agency agrees, CASA will abandon its court application and lift the airline's suspension - setting Tiger up for a restart of its domestic operations next week.

In a statement just issued, the Civil Aviation Safety Authority said the airline "has responded positively" to its demands.

"CASA's investigations have been completed and a set of proposed conditions to be imposed on Tiger Airway's air operator's certificate have been served on the airline.

"A number of conditions must be met before CASA can be satisfied it is safe to allow Tiger to resume operations," the agency said.

"Tiger Airways has responded positively and has been providing CASA with the evidence necessary to demonstrate how it will meet the conditions.

"Once Tiger Airways has submitted, and CASA has verified, all of the documentation required, CASA will be in a position to decide whether to lift Tiger's suspension," the agency said.

The airline said this morning's move for a hearing adjournment to Friday was "by consent" between the parties.

"Tiger Airways Australia and CASA are currently in ongoing discussions regarding the suspension and see no utility in having a hearing today whilst these discussions continue," it said in a by-now familiar statement wording.

"Tiger Airways Australia flights will, by virtue of the adjournment, remain suspended until August 5," it said.

The five-week grounding has cost the airline about AU$10 million so far, as well as costing its local chief executive, Crawford Rix, his job. The head of the Australian operations parent company, Tony Davis, has relocated to Melbourne from Singapore to lead the crisis talks, prompting speculation about his long-term future.

The grounding has also sparked speculation the airline will quit flying from Avalon Airport, drawn fire from consumer watchdogs over ticket sales and refunds, and cost pilots and contract staff a large proportion of their income.

The airline also faces a tough task to rebuild faith with the flying public, should it be given the green light to fly again.