NEW DELHI (REUTERS) - India's InterGlobe Aviation , owner of IndiGo airline, has shown unsolicited interest in buying a stake in state-owned carrier Air India, television channel CNBC-TV18 reported.

Several other airlines, domestic and international, have also expressed interest in buying a stake in Air India, CNBC-TV18 reported, quoting civil aviation ministry officials. The report did not name the other airlines.

A spokesman for IndiGo, India's biggest carrier by market share, declined to comment.

Shares in InterGlobe fell as much as 3.8 per cent after the news, and were down 2.4 per cent at 0947 GMT (5.47 p.m. Singapore time) in a firmer Mumbai market.

India on Wednesday gave approval to privatise debt-laden Air India, the first step of a process that could see the government offload an airline struggling to turn a profit in the face of growing competition from low-cost rivals.

The approval, the first of a series of steps needed before Air India can be sold, signals Prime Minister Narendra Modi's determination to fend off union opposition and sell an asset some economists have long argued should be in private hands.

India will now form a committee to decide on the details, Finance Minister Arun Jaitley said on Wednesday, including the size of the stake to be sold and whether the government should write off part, or all, of Air India's 520 billion rupees (S$11 billion) in debt - a step some officials say is a must to attract buyers.

Air India was bailed out in 2012 with $5.8 billion of federal funding.

Previous attempts to sell the state-owned airline have floundered, in part due to a lack of potential buyers.

Once India's biggest airline, Air India's market share in the booming domestic market has slumped to 13 per cent as private carriers such as IndiGo, SpiceJet and Jet Airways expanded.

Low-cost carrier IndiGo has a 40 per cent share of the domestic market.