Kingfisher chairman and brewing magnate Vijay Mallya said the carrier was examining the offers, according to the Economic Times, a leading Indian financial daily.
The chosen investor would pick up a 24 percent stake in the Bangalore-based carrier if a deal was reached, Mallya said, declining to identify the candidates.
"They are large investors, and I would leave it there," he said.
The company owes suppliers, lenders and staff millions of dollars but Mallya said no agreement had yet been reached with the airline's existing bank lenders on its requests for more funds.
Kingfisher has scrapped scores of flights with only 28 of its fleet of 64 aircraft in operation. Many of its planes have been reclaimed by lessors or are awaiting spare parts.
The airline, India's second-largest until earlier this year when its cash woes deepened, has blamed its latest problems on officials freezing its bank accounts for not paying tax arrears.
The company's net loss widened sharply to 4.44 billion rupees ($88 million) in the three months to December from a loss of 2.54 billion rupees a year earlier. Its debt totals at least $1.3 billion.
A consortium of banks led by state-run State Bank of India was expected to meet next week to discuss whether to extend fresh loans to Kingfisher, based on a new feasibility report, domestic media said.
The banks already own about a quarter of Kingfisher through an earlier debt-for-equity swap, and bankers have said they would like to see the airline get cash injections from other investors before they put in more money.
Mallya has said closing Kingfisher "is not an option".
India's cabinet is next month expected to approve allowing foreign airlines to take up to a 49 percent stake in domestic carriers.
Analysts have mentioned IAG, parent company of British Airways, and EtihadAirways, flagship carrier of the United Arab Emirates, as firm that might be interested in a Kingfisher stake.