Rondo was waived by the Chicago Bulls in June after spending one season with the team.
ESPN's Adrian Wojnarowski added there is "real traction" regarding a possible deal and that New Orleans thinks Rondo could be on the floor at the same time as guard Jrue Holiday.
The 31-year-old Rondo struggled through an up-and-down season with the Bulls, shuttling in and out of the starting lineup.
He averaged just 7.8 points, 6.7 assists and 5.1 rebounds per game during the regular season but was key as Chicago seized a 2-0 lead over the top-seeded Boston Celtics in the first round of the playoffs.
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Rondo put up 11.5 points, 10.0 assists and 8.5 rebounds per game in those two contests, but an injury knocked him out for the rest of the playoffs, and the Bulls were ousted.
For his career, Rondo is a four-time All-Star and former NBA champion who enjoyed the bulk of his success during a run of eight-plus seasons with the Celtics.
He has bounced around to the Dallas Mavericks, Sacramento Kings and Bulls over the past three seasons and failed to consistently replicate his previous level of play.
Rondo could be a strong fit in New Orleans due to the team's need for backcourt players to complement Anthony Davis and DeMarcus Cousins.
The veteran point guard could back up Holiday or play alongside him at times for a Pels team that has missed the playoffs each of the past two seasons.