Executives of the airlines met State Bank of India officials in recent days to discuss Jet's cash flow and business plan, two of the people said. One said Jet has outstanding dues of about $400 million (314.29 million pounds), mainly owed to lessors and vendors.
Abu Dhabi-based Etihad is also considering raising its stake above the 24 percent it has held since 2013, said one of the people, who declined to be identified as the talks were private. Foreigners can own up to 49 percent of an Indian carrier.
The news sent Jet's stock up as much as 3 percent in early trade before closing down 5.5 percent.
Etihad declined to comment. Jet and State Bank of India did not respond to requests for comment.
Jet, controlled by founder Naresh Goyal, is India's biggest full-service carrier by market share, serving one of the world's fastest-growing domestic aviation markets.
Yet the market is dominated by low-cost carriers such as Interglobe Aviation Ltd IndiGo, and is blighted by high fuel prices, a weak rupee and price competition.
More cash from Etihad is not guaranteed considering its own financial state, one of the people said. The airline reported a $1.52 billion annual loss for 2017 due in part to insolvency partnerships Alitalia and Air Berlin PLC.
However, there is also the fear that Jet will struggle to survive without further investment, the person said.
Etihad's board meets on Friday and could discuss the airline's Jet investment, one of the people said.
"Should the board decide something, it has to go to the executive council of Abu Dhabi for approval and that would take some time," the person said.
Discussions between the two airlines and India's biggest state-run bank focused on operational cash flow, said one of the people. The executives want clarity on how much more debt Jet can take on, and the bankers want to know how much equity the airlines can provide, the person said.
Jet, whose debt was about 80.52 billion rupees (893.70 million pounds) as of Sept. 30, is seeking funds at a time of tighter lending standards and a general liquidity crisis in India.
The airlines also presented a business plan detailing Jet's network and fleet expansion targets over three to five years, as well as revenue and cost projections, one of the people said.
There is an indication that by mid-January the airline could see some money coming in, said the person, without elaborating on the source of funds. At present, Jet does not have the liquidity to honour all payments and expenses but is paying statutory dues such as taxes, the person said.
The airline has delayed salary payments to pilots and top executives and is cutting flights on non-profitable routes to save money.
With fewer flights, Jet aims to reduce airport and support staff, the person said. The airline has also deferred delivery of at least two aircraft to January from November-December, the person added.
Some domestic airport operators and fuel suppliers have put Jet on cash-and-carry, meaning it must pay cash in advance for services used, the person said.
(Reporting by Aditi Shah in NEW DELHI and Stanley Carvalho in ABU DHABI; Additional reporting by Chris Thomas in BENGALURU; Editing by Muralikumar Anantharaman and Christopher Cushing)
By Aditi Shah and Stanley Carvalho