Tata said in a statement that it would not comment on speculations. Jet Airways did not respond to a request for comment.
Shares in Jet Airways surged on the news report, closing up 10 per cent on Monday.
India's aviation market is growing at 20 per cent annually, but a combination of rising oil prices, high fuel taxes, a weak rupee, low fares and intense competition have driven carriers into the red.
Jet Airways is making losses and is struggling to pay salaries and meet aircraft lease payments. The airline, which is seeking a cash injection, said in August it would cut costs in excess of Rs 20 billion ($274 million) in two years and planned to raise funds by selling a stake in its frequent flyer programme.
Tata already owns two airline ventures in India - full-service carrier Vistara, in partnership with Singapore Airlines and AirAsia India, along with AirAsia Berhad.
Tata aims to merge Jet with Vistara, sources told CNBC-TV18.
It would also buy Jet Airways' loyalty programme Jet Privilege.