Reuters reported this month that Tsai was in advanced talks to buy a stake in the Nets, which Tsai subsequently denied.
The deal values the U.S. basketball team at around $2.3 billion(£1.75 billion), the sources, who declined to speak for attribution because they are not permitted to speak to the press, said.
Under the terms of the deal, Tsai would have the option to buy a controlling interest in the next few years, the sources said.
A spokeswoman for the Brooklyn Nets declined to comment.
A deal would make the Brooklyn Nets the second NBA team to be worth more than $2 billion, demonstrating the increasing value of these teams as TV networks and advertisers pour money into live sports.
As more viewers choose to watch their favourite shows "on demand," live sports still drive people to watch the games in real time - which is valued by advertisers who have time-sensitive promotions.
In September, American casino mogul Tilman Fertitta bought the Houston Rockets for $2.2 billion, the highest price ever paid for an NBA team, according to media reports.
(Editing by Anna Driver and Susan Thomas)
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