The Athletic reported last month Kyrie Irving and Kevin Durant were "pushing" the front office to bring in Anthony.
Livingston played a key reserve role for the Warriors the past five seasons, averaging 5.9 points and 17.6 minutes in 102 postseason games.
Kevin Durant has explained his exits from the Oklahoma City Thunder and Golden State Warriors, claiming he sometimes hates the NBA "circus".
"Am I willing to accept a certain role on a basketball team? Yes," Anthony said on ESPN's "First Take" earlier this month.
The Nets signed Chandler to a one-year, $2.5 million contract alongside Kyrie Irving, Kevin Durant and DeAndre Jordan this summer.
Wing Caris LeVert will be staying with the Brooklyn Nets for the foreseeable future after agreeing a reported three-year extension.
Brooklyn and the wing agreed to a three-year, $52.5 million deal that will begin with the 2020-21 season, according to a report from ESPN.
Lakers forward Kyle Kuzma was the final cut as he's dealing with a left ankle injury that prevents him from competing in the tournament.
Billionaire Joseph Tsai, who already owned 49 per cent of the Brooklyn Nets, has bought the rest of the NBA franchise.
Green said Durant didn't owe it to anyone to disclose how he was handling his free agency.