But another source close to the situation said unless the Cowboys are offered significant value in return, they are unlikely to trade Jenkins, who is entering the last year of his contract.
Cowboys executive vice president Stephen Jones said the Cowboys haven't fielded any calls for Jenkins, and the team hasn't made any calls, either.
"We think the world of Mike Jenkins," Jones said Friday afternoon. "He is going to be an important part of the team, more than likely, for us this year. ... At the end of the day, I think he will be on our team."
Jenkins' long-term status with the Cowboys became cloudy after the team drafted cornerback Morris Claiborne with the sixth overall pick Thursday night.
Jones said he talked to Jenkins' agent, Drew Rosenhaus, on Thursday night.
"We were trying to win the NFC East championship, unfortunately, with [backup] guys like Alan Ball and Frank Walker," Jones said. "I'm not trying to be rough on them, but guys get hurt. And we would like to have good players that are available, and Mike Jenkins is a damn good cornerback."
Jenkins, a first-round pick in 2008, is recovering from shoulder surgery. He's projected to return in time for training camp, and has been "in and out" for voluntary workouts at the team's practice facility in Valley Ranch, Jones said.
"[He's] taking care of some business, and we need him to get back here and get to work with the rest of his teammates."
Jenkins was one of five cornerbacks to play for the Cowboys last season and finished with one interception and was tied for the team lead with 10 pass breakups. The team currently has four cornerbacks on the roster -- Brandon Carr, Orlando Scandrick, Claiborne and Jenkins.
When the Cowboys traded from No. 14 to No. 6 with St. Louis on Thursday to get Claiborne, they also gave up a second-round pick. The Cowboys would like to get back into the second round, but it's unknown if they can get a second-round pick, or another pick later in the draft, in exchange for Jenkins.
The additions of Claiborne and Carr have provided more depth at a position where the Cowboys struggled last season. Scandrick also was given a five-year contract extension prior to the 2011 season.
Rosenhaus has sought a contract extension for Jenkins this spring. And while the Cowboys were open to it, there's been no movement on a new deal.