Carr is set to count $12.7 million against the salary cap during the 2015 season and the Cowboys have been trying to restructure his contract to lower that figure.
"That one is as it is, we're evaluating, looking to the extent that we can make contractual adjustments that would fit and help us under the cap, we want to try to do that with him," Jones said. "We value Carr and what he can mean for us this year."
Carr has refused to discuss his contract status publicly and Jones said restructuring the deal remains a priority.
"All of the contracts that we don't have closure on are a priority," Jones said. "He certainly is a player who is in our top consideration. So yeah, I'd say that's a priority. We want him on the football field."
"Some things I don't discuss out in public," Carr said. "This is one of those."
Carr will count $12.7 million against the cap during the 2015 season if he does not restructure his contract and he declined to say if he'd be willing to lessen the amount.
"I'm still here,'' he said. "I'm here until told otherwise. That's my philosophy. At the end of the day, if I'm playing football then I'm going to give my all for whoever I'm playing for."
When asked if the team would attempt to ask him to take a pay cut, Jones replied, "No, not yet."
Late last week Carr's agent, Ben Dogra, said that the corner would not be willing to take less money.
Carr, 28, has played seven years in the NFL for the Chiefs and the Cowboys. In that time he has 415 total tackles, 95 passes defensed, 14 interceptions and one forced fumble.
Carr signed a five-year, $50,100,000 contract in 2012. The next year he converted over $13 million of his salary into a signing bonus to free up cap space.
The 28-year-old cornerback has played seven seasons in the NFL, registering 415 total tackles, 95 passes defensed and 14 intercepitons. He has never missed a start since joining the league in 2008.
|2008||Kansas City Chiefs||16||73||70.0||3||0||2||67||33.5||35||0||6|
|2009||Kansas City Chiefs||16||62||56.0||6||0||1||31||31.0||31||0||19|
|2010||Kansas City Chiefs||16||57||46.0||11||0||1||0||0.0||0||0||25|
|2011||Kansas City Chiefs||16||45||39.0||6||0||4||17||4.2||14||0||15|
|Year||Team||G||Fum||Lost||Fum Forced||Own Rec||Opp Rec||Yds||Tot Rec||TD|
|2008||Kansas City Chiefs||16||0||0||0||0||2||17||2||0|
|2009||Kansas City Chiefs||16||0||0||1||1||1||1||2||0|
|2010||Kansas City Chiefs||16||0||0||0||1||1||23||2||0|
|2011||Kansas City Chiefs||16||0||0||0||0||0||0||0||0|
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