Jenkins has remained home in Florida while rehabilitating from shoulder surgery. There are numerous reports that Jenkins wants to be traded, though coach Jason Garrett said that is not going to happen.
"Mike Jenkins, we believe, is a big part of our football team right now," Garrett said Wednesday. "He's making a business decision not to be here, but we're not going to trade him. ... We've got to get him healthy, we've got to get him back getting going."
Jenkins is going into the final year of his contract after the Cowboys added two prominent cornerbacks. Brandon Carr got a $50 million, five-year deal in free agency. The team also traded up and gave up a second-round pick in the draft to get LSU All-American cornerback Morris Claiborne sixth overall.
Jenkins started 12 games last season, missing four with a hamstring injury. The additions of Carr and Claiborne presumably will take Jenkins out of the starting lineup.
"We're concerned about Mike Jenkins' health first and foremost. ... We've been in communication with him, and he seems to be getting better. We want Mike Jenkins around our team," Garrett said. "We had 60 guys on our roster for most of the offseason, and we had 59 guys at our facility working out, involved in our offseason program."
The two-hour workout Wednesday was the first open to the media, and came a day after Jerry Jones told the NFL Network during the owners meeting in Atlanta that he feels like the Cowboys' window to contend for a title with players like Ware, quarterback Tony Romo and tight end Jason Witten was "getting shorter."
Jones watched practice Wednesday, but left without talking to reporters.
"My experience in this league as a player and coach, the best players and the best teams have a sense of urgency every single day in all that they do," Garrett said.
Claiborne is recovering from left wrist surgery that he had before the draft and is wearing a soft cast. He may not be ready for full workouts until the start of training camp in late July.
Fifth-round pick, receiver Danny Coale, broke his left foot during practice Tuesday. He will have surgery Thursday, though Garrett said he should be able to recover in time for training camp.
The Cowboys have two more weeks of voluntary workouts before a mandatory veteran minicamp June 12-14, and Garrett expects Jenkins to be there.
"We've been in communication with Mike, we want Mike to be here and when he has to be here, he will be here," Garrett said. "We'd like to have him before then, but that's his decision right now."
New secondary coach Jerome Henderson said he has had some good conversations with Jenkins by phone.
"Obviously he's missing a lot because we've got some new things this year," Henderson said. "I'm missing getting a chance to know him on the field better, and he's missing a chance to get to know me. ... Mike's a pro, and once he gets that situation settled, I'm sure he'll be in here ready to work and ready to go."
Notes: DeMarco Murray, the team's leading rusher with 897 yards last season despite missing the last three games with a broken right ankle, said he feels great and has no limitations. ... RB Felix Jones has a shoulder injury that is keeping him from full participation. ...WR Dez Bryant says it was frustrating last season to get hurt early (thigh bruise) after having his rookie season in 2010 shortened by a broken right leg. "I don't think I was ever where I wanted to be," he said. He said he's spending more time focusing on his body and making sure everything is right.