The Bulls have been in talks with Parker's agent, Chicago-based Mark Bartelstein.
The contract is for two years and $40 million, a rather high price to pay for someone with large injury concerns and a lack of playing time in his first four seasons.
Updating a previous item, the Bucks did not rescind Jabari Parker's qualifying offer, according to Matt Velazquez of the Milwaukee Journal-Sentinel.
The Milwaukee Bucks weren't going to match an offer sheet to Parker, so they rescinded their qualifying offer to allow him to sign a shorter deal. Parker, a Chicago native, will be heading back to his hometown to continue his career.
Parker is now a restricted free agent and the Bucks have extended him the one-year qualifying offer of $4.3 million. He only played in 31 games for the Bucks last season.
Parker, who was selected No. 2 overall in the 2015 NBA Draft, averaged 12.6 points and 4.9 rebounds per game last season.
During that season, the forward averaged 20 points, six rebounds and almost three assists in 50 games before suffering a knee injury. The Bulls had made two earlier moves, trading Jerian Grant and Julyan Stone in order to free up even more cap space.
The former Pistons standout was back in the Detroit area Friday night as part of the BIG3 - entertainer Ice Cube's 3-on-3 league of former National Basketball Association players, which made a stop at Little Caesars Arena. The Bulls appear to have an offer on the table for Parker.