Jenkins, recovering from offseason shoulder surgery, has attended only a handful of voluntary workouts and while team officials wish he would come to Valley Ranch to work out, they have said it's not a requirement.
A league source had previously told ESPNDallas.com the Cowboys shopped Jenkins after drafting Morris Claiborne, but another source close to the situation said Dallas was reluctant to deal Jenkins unless it received a substantial return.
Team owner Jerry Jones said two weeks ago he would like to sign Jenkins to a long-term deal.
In 2011, Jenkins was tied for the team lead with 10 pass breakups and finished with one interception in an injury-riddled season that saw him battle knee, neck and shoulder injuries.
With the Cowboys signing cornerback Brandon Carr to a five-year, $50.1 million deal and moving up in the draft to select Claiborne with the sixth overall pick, it seems Jenkins' role as a starter is coming to an end.
Jenkins, as it stands now, is probably the third corner.
"Mike Jenkins gave me everything he can," defensive coordinator Rob Ryan said recently. "He had a blown shoulder. He had everything going on. He played his heart out. But half the games he wasn't there, which is unfortunate, because he's a super talented guy. I think we were banged up there at that position. We had every kid on our roster playing corner for us. We've got obviously two fantastic players to help us and that's exactly what they're going to do."