Gasol averaged 17.4 points and 9.7 rebounds in 60 games for the Lakers in 2013-14, the final year of a three-year, $57 million contract.
The Bulls, who won 48 games and earned the No. 4 seed in the Eastern Conference before getting knocked out by the Wizards in the first round of the playoffs, were rumored to be in contention to land free agent forward Carmelo Anthony but he is close to re-signing with the Knicks.
Chicago is reportedly close to reaching a deal with European forward Nikola Mirotic.
The team also features 2014 Defensive Player of the Year Joakim Noah and sixth man of the year runner-up Taj Gibson in its frontcourt.