Gibson is coming off his sixth season with Chicago. This season he averaged 10.3 points, 6.4 rebounds and 1.2 blocks per game while shooting 50.2 percent from the field.
Gibson has two seasons remaining on the four-year, $38 million extension he signed in November 2012.
The 29-year-old missed time this season with ankle issues, but started 17 games and appeared in 62.
The Bulls went 50-32 and earned the No. 3 seed in the Eastern Conference before being eliminated in the second round of the playoffs by the Cleveland Cavaliers.