The deal is worth $3 million but could reach a maximum of $3.75 million, the source said.
The Cowboys surprised many by moving up to the sixth overall pick in the 2012 draft to select Claiborne, who won the Jim Thorpe Award as the nation's best defensive back out of LSU. At the time, the Cowboys said Claiborne was their highest-graded cornerback available in a draft since Deion Sanders.
In his four seasons with the team since, Claiborne intercepted three passes.
The Cowboys chose not to pick up the fifth-year option on Claiborne's contract last spring, making him a free agent this offseason.
Injuries played a big part in the 26-year-old Claiborne's lack of production. He arrived in Dallas with a surgically repaired wrist and missed time in training camp with knee soreness. He missed one game as a rookie in 2012 because of a concussion, six games in 2013 because of a hamstring strain and 12 games in 2014 because of a torn patellar tendon that required rigorous rehab.
Claiborne started the first nine games in 2015, but he suffered a hamstring strain and ankle injuries that forced him to miss five of the final seven games.
For Claiborne's career, Cowboys coaches credited him with 144 tackles, one tackle for loss, one quarterback pressure, 27 pass deflections, one forced fumble and three fumble recoveries.