Jones said in an interview on 105.3 The Fan in Dallas that he believes in Kiffin, defensive line coach Rod Marinelli and the rest of the Cowboys' defensive staff.
"To fix what we're doing, there's nobody I'd rather have than him and Rod Marinelli, and where we are today to get this fixed over the next week, two weeks, three weeks," Jones said.
"There's nobody I'd rather have than him to fix it. First of all, he knows what we're doing better than anyone, and if there are adjustments to be made, he's the right man for the job right now."
Asked about an in-season firing, Jones said he expects Kiffin to get to work at improving the defense to get the Cowboys to the play-offs.
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Minnesota Vikings running back Adrian Peterson will not have surgery on his sprained right foot after an initial round of tests showed no Lisfranc injury.
According to multiple media reports, Peterson's playing status will be determined if and when he gets out of walking boot.
Peterson suffered a mid-foot sprain when his right foot was trapped under Baltimore Ravens linebacker Arthur Brown while being tackled early in the second quarter of Sunday's snowy 29-26 loss.
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Green Bay Packers quarterback Aaron Rodgers is unlikely to play this week, and he acknowledged experiencing a setback last week in his rehab.
Rodgers, out since breaking his collarbone in a November 4 game against the Chicago Bears, felt pain while practicing with the team last Wednesday, he said Tuesday on WAUK-AM radio.
"I shouldn't be having pain doing some of the simple movements," Rodgers said. "It didn't get better as the week went on. I tried a lot on Wednesday; it didn't feel good. ... It's frustrating, very frustrating. I was trying to push it before science tells you before it's possible."
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The Cleveland Browns have waived backup quarterback Caleb Hanie and signed running back Edwin Baker off the practice squad of the Houston Texans.
The moves indicate that the Browns probably expect running back Willis McGahee to miss time with a concussion he suffered Sunday in a loss to the New England Patriots and quarterback Brandon Weeden to return from a concussion he suffered December 1 against the Jacksonville Jaguars.
Hanie, a sixth-year veteran whom the Browns signed a week ago, served as starting quarterback Jason Campbell's backup this past weekend with Weeden sidelined.
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The Miami Dolphins have placed starting cornerback Dimitri Patterson on season-ending injured reserve.
Patterson battled a groin injury most of the season and re-injured it in Miami's 34-28 victory Sunday over the Pittsburgh Steelers.
The Dolphins also placed backup cornerback and special teamer R.J. Stanford on season-ending injured reserve with a broken fibula. Miami signed free agent cornerback Justin Rogers and safety Michael Thomas off the San Francisco 49ers' practice squad to take their place on the roster.
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The Buffalo Bills have activated defensive back Jonathan Meeks from injured reserve/designated for return to the 53-man roster and released linebacker Jamaal Westerman.
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The San Francisco 49ers placed defensive tackle Tank Carradine on injured reserve.
To fill Carradine's spot on the active roster, the 49ers signed guard Ryan Seymour from the Seattle Seahawks' practice squad to a three-year contract.
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The Washington Redskins have promoted running back Jawan Jamison to their active roster and signed free agent running back Miguel Maysonet to their practice squad.
In addition, the team placed backup running back Evan Royster on injured reserve with ankle injury.