Tata, Indian publisher Mint reports, is understood to be conducting due diligence ahead of a move.
Reports in India suggest Jet chairman Naresh Goyal approached potential investors last month.
A source close to the negotiations, Mint reports, said Goyal, who founded the airline, was willing to cede control.
Neither Tata nor Jet have so far commented on the reports.
Jet Airways currently flies from Heathrow airport to Delhi and Mumbai, and from Manchester airport to Mumbai, Abu Dhabi, Paris and Amsterdam.
