The financial daily said the country's aviation ministry had given its approval to the move in principle with further discussions to determine what level of investment would be allowed.
If approved, the move could help inject much-needed capital into private Indian airlines, which have been struggling with increased competition, rising fuel costs and a falling rupee in recent months.
Currently, foreign airlines are banned from investing in Indian airline firms either directly or through equity markets. But foreign institutions can buy shares in India's listed airlines Kingfisher, Jet Airways and SpiceJet.
The newspaper said the Department of Industrial Policy and Promotion, which frames policy on foreign investment, was in favour of overseas carriers taking up to a 26 percent stake in Indian airlines.
But the civil aviation ministry preferred a lower, more restrictive cap of 24 percent, it added.
India's airlines have been growing at an average of 15 percent each year since 2006, analysts say.
Kingfisher Airlines said last month that it was cutting its low-cost operations to concentrate on full-fare flights in a bid to cut losses.
State-run Air India has also been struggling with debt.