Sources: Cowboys RBs draw interest
However, a league source told ESPN.com's Matt Mosley that the team is not going to trade Barber, the starter at the position.
Drew Rosenhaus, Barber's agent, told ESPNDallas.com that he hasn't heard from the Cowboys or other teams regarding a possible trade.
Cowboys officials must cut their roster down to 53 players by 3 p.m. CT Saturday.
Barber, who has led the team in rushing the last three seasons, hasn't performed as a dominant running back because of injuries he's endured the last two years.
Trading Barber is difficult as well because he has a huge contract. In the spring, he received a $4 million roster bonus and is owed $3.8 million in base salary this year.
Barber is also due to make $14 million through 2014. But it appears doubtful that he will play to the life of his current contract.
Earlier in the day, the Cowboys traded wide receiver Patrick Crayton to the San Diego Chargers for a seventh-round pick. Dallas also traded guard Pat McQuistan to the Miami Dolphins for a sixth-round pick.
Before the deals were announced Friday, Cowboys owner and general manager Jerry Jones said there was a chance a trade was forthcoming.
"I'd say possible," he said. "Possible, but very real."
The Cowboys have been in a cost-cutting mode this week. They saved $3.17 million in base salaries by releasing safety and special-teams ace Pat Watkins and dealing Crayton.
If the Cowboys let Barber go, either by trade or release, the move would increase their savings to roughly $6.2 million.
"It's not strictly the money," team executive Stephen Jones said. "It's how do you want your team to progress, and if you're always keeping the veteran guys over the young guys you ultimately become an old team. And that bites you at some point."
The Cowboys could go younger at running back by using Felix Jones as the starter and moving Choice, the team's No. 3 running back, to a backup role. For the moment, the Cowboys appear ready to start the season with Barber.