Vickers, a six-year veteran from Beaumont, Texas, played in 14 games last season. He only had one carry and had two special teams tackles for the Texans.
Vickers was the lead running back for Arian Foster, who rushed for 1,224 yards and 10 touchdowns last season.
The Cowboys were also in talks with fullback Tony Fiammetta and declined to give him an exclusive rights deal on Tuesday. What this means for Fiammetta's future with the Cowboys is uncertain.
It appears doubtful the Cowboys would want Vickers and Fiammetta, two veterans on the team.