Tata has sought management control of Jet, seeking at least 26 percent initially and another 26 percent via an open offer later, the paper said.
Jet Airways has been facing a financial crunch amid rising oil prices and a depreciating rupee. In a bid to revive itself, Jet said in August it will inject funds and cut costs to turn around the business, without elaborating further.
A Jet Airways representative said the news report was speculative, while the Tata Group declined to comment.
Tata Sons [TATAS.UL] is the holding company for the Tata Group which already has two aviation ventures in India - Vistara with Singapore Airlines (SIAL.SI) and AirAsia India with the Malaysian budget carrier AirAsia Group (AIRA.KL).
Jet Airways Chairman Naresh Goyal is the majority owner of the airline in which Etihad Airlines also owns a stake.
The struggling airline has also not been able to pay salaries to the employees on time.
Reporting by Tanvi Mehta in Bengaluru; Editing by Gopakumar Warrier