DALLAS -- The speculation surrounding whether the Dallas Cowboys are shopping starting running back Marion Barber is just that.

Multiple team sources said Tuesday that the Cowboys haven't discussed trading Barber, who is coming off two injury-filled seasons where he failed to rush for more than 1,000 yards. The NFL Network reported Monday that NFL executives have said Barber is available via trade.

Barber is scheduled to get a $4 million roster bonus and a $3.8 million base salary in 2010. If the Cowboys trade Barber, another team would have to pick up that contract or try to rework the deal.

The only definitive information about Barber's status has come from Cowboys owner and general manager Jerry Jones, who said the organization has thought about starting Felix Jones.

"I see the advantages the way we've done it," Jerry Jones said last week about having started Barber with Felix Jones in a reserve role. "But it was a pretty close decision, really. I know it was a consideration."

Barber, who doesn't give interviews, has been working out at the Michael Johnson Performance Center in McKinney, Texas, to get in better shape.

Last season, Barber suffered from a plethora of injuries -- a bruised left thigh, fractured thumb and a bruised left knee -- but missed just one game, Week 3 versus Carolina.

Jerry Jones is not concerned about Barber's health.

"It would [concern me] if we didn't have the depth there," Jones said. "But by having the depth, we can feel good about [it]. Maybe [if] Marion hadn't [had] a couple of unfortunate seasons there, maybe we'll get a big year out of him. If you did that, you've hit a home run."

Backup running back Felix Jones finished his second season with 685 yards and three touchdowns on 116 carries. In two playoff games, he led the Cowboys' rushing attack with 217 yards and a touchdown on 30 carries.

Tashard Choice, the No. 3 back, is used on third down and in the Razorback formation, but he would like to get more carries in the offense. Choice has expressed frustration with his role, but he hasn't asked for a trade.

The Cowboys have been scouting running backs for the upcoming draft. If they select one, it would create a logjam at an already-crowded position.

Stephen Jones, the Cowboys executive vice president, said last month he expected the team to keep all three of its running backs.

"I know this: We've been doing what we ought to be doing and that's evaluating the running game and how we're the most productive ... what plays, what formations give us the most production," Jerry Jones said. "Based on preliminary input from our coaches, you could certainly see Felix in there earlier."

Calvin Watkins covers the Cowboys for ESPN Dallas. You can follow him on Twitter or leave a question for his weekly mailbag.