Claiborne was the second-highest rated player on the Cowboys' draft board, following quarterback Andrew Luck.
Will the Cowboys move up in 2013?
Cowboys executive vice president Stephen Jones doesn't believe it'll happen.
"I don't think so, but I wouldn't totally rule it out," Jones said on KZDC-AM San Antonio on Tuesday afternoon. "Typically you save those big move ups for your skill players ... whether it's a corner or a pass-rusher on defense, a quarterback, running back, receiver. You're usually willing to give up a player later in the draft to really get a guy you want. I don't necessarily see that for us this year."
This year's draft is deep along the offensive and defensive lines and at defensive back.
The Cowboys have needs at those positions, but with the draft being so deep in certain areas, Cowboys owner/general manager Jerry Jones said he's willing to trade down from No. 18. But they do have priorities.
"I think protecting our big investments probably first and foremost, our commitment of resources we made to (Tony) Romo," Stephen Jones said on KZDC-AM. "What you want to do is keep him standing up and healthy, and if the right situation occurs there to help protect him in the offensive line, you've got to take a look at that. At the same time, you can't compromise the integrity of your board."