Air India faces competition from other airlines
Air India says it is considering offering leave without pay to as many as 15,000 of its workers for a period of up to five years.
The state-owned airline stressed that the option would be voluntary.
Air India's Managing Director Raghu Menon told the PTI news agency that those who take up the possible offer would be allowed back on the same pay.
India's once booming aviation sector has been hard hit by soaring costs, mainly due to global fuel price rises.
Hundreds of staff sacked by Jet Airways, India's largest private airline, have held more protests following the announcement on Wednesday that it was laying off 1,900 employees to cut costs.
Over 200 staff in Mumbai (Bombay) protested outside the Jet Airways head office, supported by members of the Maharashtra Navnirmaan Sena party who are campaigning against the job losses.
Jet Airways staff have held protests
The BBC's Prachi Pinglay in Mumbai says that the protesters only dispersed when the Jet Airways Chairman, Naresh Goyal, agreed to hold a meeting next week with the Maharashtra Navnirmaan Sena party leader, Raj Thackeray.
A similar protest by Jet Airways staff - wearing their distinctive bright yellow uniforms - was also held in Delhi.
The BBC's Sanjoy Majumder in Delhi says that the news of the job losses has come as a shock not just to airline employees but also to some in government.
Our correspondent says that the good times for Indian airlines may be about to end.
In the past few years, India's private airlines offered Indians a chance to travel by air offering them low cost fares.
But that was placed in jeopardy earlier this week when it was announced that Jet Airways was forming an alliance with the country's other largest private carrier, Kingfisher Airlines.
Air India insists that its jobs reduction plan is not mandatory and is not a retrenchment.
Indian airports may be a little quieter in the months ahead
The company says that those who return after a leave of absence will be provided jobs at the same seniority and pay as when they left.
Officials say that the proposals will soon be presented to the company's board.
Civil Aviation Minister Praful Patel has stressed there were no plans compulsorily to prune staff numbers which currently total about 25,000 people.
"Air India is not going to have any job cuts. Certainly it [the aviation crisis] will affect the growth plans, it will affect the future employment opportunities which would have come the way of Air India in case the aviation industry was in a much better financial health," Mr Patel told PTI.
"But as of now I do not have the luxury to say [anything] beyond the fact that those who are working for Air India shall continue to do so and we shall not have any issue of people being laid off."