Smith was removed from the PUP list by the Bears on Wednesday.
Smith said in a written statement that he has requested a trade after contract negotiations with the team reached an impasse.
Smith was expected to hold in until he and the Bears reached an agreement after he reported to training camp. The former first-round pick is in the final year of his contract, and he is set to make almost 10 million dollars.
While waiting for a new contract, Smith participated in the entire Bears summer workout program and did not appear to suffer an injury. The player has been present for all 12 training camp practices and has been doing rehabilitation exercises near the weight room.
The collective bargaining agreement requires the National Football League to pay players their full salaries while they are on the physically unable to perform list. Smith can be fined $40,000 a day if he skips practice. While waiting for new contracts, Seattle wide receiver DK Metcalf and San Francisco wide receiver Deebo Samuel held out at training camp, but were not fined by their organizations.