A deal, which the official said could be announced by next week, would be the first since the government relaxed ownership rules in September -- allowing foreign airlines to invest up to 49 percent in a domestic carrier.
"Etihad has not yet decided. They are talking to both," said the official, who has knowledge of the talks but declined to be named as the negotiations are confidential.
The decision is now with the board of Etihad and Abu Dhabi's state-owned investment fund Mubadala, said one Dubai-based source who did not want to be identified for the same reason.
Indian financial firm Edelweiss is advising Kingfisher, the firm and the airline's management team have met with Etihad several times over the last few days.
Buying into Jet is seen as more lucrative for Etihad as the two carriers already have a code-sharing agreement and could target the market share of state-owned Air India and Dubai-based Emirates Airline, the latter of which dominates routes between India and the Middle East.
But a stake in Kingfisher, which has been grounded after its licenses were suspended and whose owner, liquor baron Vijay Mallya, has been looking for an investor for more than a year, would be cheaper.
The Dubai-based source said news leaked on the Jet-Etihad partnership plans shot up the stock price, causing the Abu Dhabi carrier to reconsider.
Shares in Jet Airways Ltd, the No. 2 Indian carrier, closed 2.4 percent higher on Monday, after rising as much as 4.7 percent to a nearly two-year high, on hopes that Abu Dhabi-based Etihad would strike a deal with it.
Kingfisher shares were down 5 percent.
"Unbelievable as it might sound, Kingfisher at the moment stands a better chance, but the price has to be right," said Rajan Mehra, an industry expert and the India head of U.S.-based private jet operator Universal Aviation.
Adding, "Etihad will be able to have control over the airline. Right now what they want is control," said Mehra, who previously headed Qatar Airways' India operations.
The debt-laden carrier said last week it was in talks with Etihad and other investors about taking a stake, while later in the week it capped foreign portfolio investment in the company at 3 percent, carving space for a foreign investor to buy as much as 49 percent in it.