If it goes through as reported, the sale would mark the highest ever paid for a sports franchise.
Tsai reached his deal to buy the minority stake in 2017 for $1 billion that reportedly came with the option to buy the remaining stake for $1.35 billion prior to the 2021-22 season. The team declined to comment about the report in the Post.
Anthony, who played parts of seven seasons with the New York Knicks, would be the latest in a long line of stars at various stages in their careers who've joined the Brooklyn Nets franchise this summer.
The $2.35-billion figure becomes the most expensive purchase for a North American sports franchise, surpassing the $2.2-billion acquisitions of the Carolina Panthers and Houston Rockets - both in 2018.
Joseph Tsai had wanted to get into the National Basketball Association game for a while and, back in 2017, put his money where he mouth was and spent $1 billion to buy 49 percent of the Brooklyn Nets.
Joseph Tsai is closing in on an agreement to purchase the controlling interest in the Brooklyn Nets from majority owner Mikhail Prokhorov, sources confirmed to ESPN.
Prokhorov bought the Nets in 2010 and the Russian oversaw the Nets' move from New Jersey to Brooklyn.
A native of Taiwan, Tsai is worth an estimated $9.9 billion after he co-founded Alibaba, the Chinese equivalent to Amazon.