ESPN.com was first to report that the Nets were expected to sign Collins.
Collins would become the first active openly gay player in the NBA. The Nets play the Lakers in Los Angeles on Sunday night. Collins revealed at the end of last season he is gay, but he was a free agent and has remained unsigned.
"Hope everyone is enjoying their Sunday. Today should be a pretty cool day!" Collins' twin brother, Jarron, tweeted.
The 35-year-old center played in 38 games for Boston and Washington in 2012-13. He has a number of former teammates on the Nets, including coach Jason Kidd.
General Manager Billy King said earlier this week the Nets had worked out Collins and he was a candidate to fill the team's need for a post player.
King said the Nets wouldn't be concerned about any extra attention the signing of Collins would provide.
"We're going to bring in a basketball player," King said. "It's not about marketing or anything like that."
The Nets have an opening for a big man after trading Reggie Evans along with Jason Terry to Sacramento on Wednesday for guard Marcus Thornton.
The news on Collins comes as Michael Sam, the SEC defensive player of the year from Missouri who recently revealed he is gay, is taking part in the NFL draft combine. Sam's on-field workouts in Indianapolis are scheduled for Monday.
Copyright 2014 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.