According to Sean Deveney of Sporting News, the Bulls will likely have to put together a three-team trade in order to move Parker since they don't want to take on any players whose contracts go beyond this season.
Deveney added that neither the Knicks nor the Pelicans can trade for Parker in a one-for-one scenario. The Bulls don't want New York guard Courtney Lee or New Orleans forward Solomon Hill.
K.C. Johnson of the Chicago Tribune reported that the Bulls are expected to shop both Parker and center Robin Lopez prior to the Feb. 7 trade deadline.
After putting up solid numbers to start the season, Parker was on the bench for 12 of 13 games until appearing in each of the Bulls' past three contests.
Deveney noted that Parker rejoined the rotation after head coach Jim Boylen became satisfied with his effort in practice.
In 33 games this season, the 23-year-old Parker is averaging 14.8 points, 6.6 rebounds and 2.2 assists while shooting 46.2 percent from the field and 31.4 percent from long range.
Parker spent the first four seasons of his career with the Milwaukee Bucks after they selected him with the No. 2 overall pick in the 2014 draft, and he showed promise.
The Duke product even averaged 20.1 points in 51 games during the 2016-17 campaign, but injuries, including a torn ACL, plagued his time in Milwaukee. Last July, the Bulls signed him to a one-year, $20 million contract with a club option for 2019-20.
New York has made a recent habit of taking on reclamation projects. Emmanuel Mudiay, Noah Vonleh and Mario Hezonja are among the examples of high draft picks who didn't work out with their original teams.
While Parker is deficient defensively, he could be an intriguing offensive option to play alongside Kristaps Porzingis when the Latvian returns from a knee injury.
The Pels don't seem to need Parker since they already have Julius Randle and Nikola Mirotic at power forward, but Parker can play the 3, which is a position New Orleans hasn't gotten a ton of production out of.
While the Knicks (10-34) aren't in playoff contention, the Pelicans are just 3.5 games out of a playoff spot in the Western Conference, and Parker could provide a scoring boost.
Since the Bulls (10-35) reportedly want salary-cap flexibility to aid their continued rebuild, however, a team with interest in Parker will likely have to part with more attractive assets, such as draft picks or young players, in order to get him.