Any deal would be the first since India changed its rules in September to allow foreign carriers to buy stakes of up to 49 percent in local airlines, which have been battered by fierce competition and high operating costs.
Shares in both the Indian carriers continued rallies from last week, with Jet shares up about 11.5 percent and Spicejet up 13.5 percent on Monday.
The fiercely competitive Indian aviation industry lost a combined $2 billion in the last fiscal year. All but unlisted IndiGo lost money, hurt by high state taxes on jet fuel, expensive airports and regulatory uncertainty.
Talks between Jet and Etihad have been the subject of media reports citing unnamed sources.
The talks are on. This is more or less final. It may take around a month and half, the government source told reporters, referring to the Jet-Etihad negotiations.
This deal is not just about investment but also technology and partnership in many other ways, said the source, who declined to be identified.
A Jet official could not immediately be reached for comment.
SpiceJet declined immediate comment, while officials from AirAsia, Asia's largest budget carrier, could not be reached for comment.
Jet Airways shares had gained 50.6 percent in November through Friday while SpiceJet was up 17 percent on speculation of potential stake sales.
Reports of stake sale have driven stocks higher but its absurd given so much government interference in this sector, said Vivek Mahajan, head of research at brokerage Aditya Birla Money.
Heavy competition is driven in part by government-subsidised losses at state-owned Air India. However, competition has eased somewhat and airfares have risen due to the decline in cash-and-debt strapped Kingfisher Airlines, the former No. 2 operator which has not flown since the start of October.
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