The Pelicans hope to sign Rondo to a one-year deal, according to the report, and there's "enthusiasm on both sides to try and work out an agreement".
The 31-year-old point guard originally began his National Basketball Association career back in 2006-07 as a member of the Boston Celtics.
The Pelicans already brought back point guard Jrue Holiday this summer, but he could move to shooting guard if Rondo is added.
If a deal pushes through, Rondo will be reunited with Cousins.
IN teen crashes into home, killing two sisters inside
The Clinton County sheriff's department says the 17-year-old driver was arrested on preliminary charges of criminal recklessness. Haleigh Fullerton , 17, and her nine-year-old sister Callie, were in the living room watching television when the crash happened.
He was suspended for one game in early December for conduct detrimental to the team after a verbal altercation of assistant coach Jim Boylen, including towel whipping him in the face.
In 69 games with the Chicago Bulls, Rondo averaged 7.8 points, 6.7 assists and 5.1 rebounds in 26.7 minutes per game.
However, Rondo missed the rest of the series due to a broken thumb, allowing the Celtics to sweep the next four games. He averaged 33.5 minutes per night in the two playoff games, seeing his scoring jump to 11.5 points per game. After that, the Bulls waived Rondo to save about $10 million of the $13.4 million he would have made next season. He was a starter on the Celtics' 2008 championship team. He also played one season for the Sacramento Kings in 2015-16 and 46 games for the Dallas Mavericks in 2014-15 after spending his first eight-plus campaigns with the Boston Celtics.