Pondexter, 29, has missed the last two seasons due to recurring knee injuries. The Bulls likely made the move for the pick and not Pondexter, who should be waived.
Pondexter currently has one year and $3.9 million remaining on his contract.
Although Pondexter was once renowned as a solid three-and-D specialist, having hit 36.5 percent of his career attempts from distance, he's not a particularly good fit in the Windy City.
The Bulls are embracing a full-scale rebuild, and allowing Pondexter to sop up minutes on the perimeter and siphon them off from younger players who need game time to develop wouldn't jibe with the team's current mission statement.
If Pondexter is ultimately let go, he'll be on a mission to prove he can still contribute in a meaningful capacity.
But considering his last appearance on the NBA hardwood came in April 2015, contenders in need of cost-effective veteran reinforcements on the bench will likely entertain the thought of signing him with a bit of skepticism until he proves capable of staying healthy.
For the Pelicans, the move is all about flexibility.
With Pondexter's cap hit off the books and a roster spot open, New Orleans has the flexibility to chase a replacement for small forward Solomon Hill, who "could miss much of [the] regular season" after suffering a torn hamstring, according to ESPN.com's Adrian Wojnarowski.