Along with the Bulls, Rondo had previous interest from the New York Knicks and the Brooklyn Nets, but both teams have already landed point guards to their rosters after signing Derrick Rose and Jeremy Lin.
Rondo is also open minded about a return to Sacramento after leading the NBA in assists with the Kings last season, a source told ESPN.
The petulant point guard averaged 11.7 per game in 2015-16, but at 30, the Kings were not ready to offer him an expensive contract. They were instead willing to let him test the free-agent market.
He's still a smart, talented player, but given how things ended in Dallas (Rondo left before the end of a first-round playoff series with what was termed a back injury), his need to command the basketball and his inconsistent outside shooting, discovering the right fit seemed to be difficult.
Information from ESPN.com's Calvin Watkins was used in this report.