Speaking Thursday on KRLD-FM, Jones said: "I think the real question is, should he be finishing rather than beginning? In his Pro Bowl year, where he had his best year, [Barber was] finishing the game. If you recall, Julius Jones started the game. We injected the quickness of his speed there early.
"That would be the issue. It's not a question of starting as much as it is, when do you use Barber at his best? There are a lot of people, prominent people who know Barber well, who feel like he would be better served used to finish the game than really used a lot at the start."
Coach Wade Phillips said the Cowboys' running back rotation will not change.
Phillips said it's important to substitute enough to prevent a workhorse runner like Barber from wearing down.
But the coaches don't intend to alter Barber's role as Dallas enters the last quarter of its schedule tied for the NFC East lead with Philadelphia.
"He's able to carry the load," Phillips said. "We want the power guy early in the game to start out to physically attack the other team, I think, and you want the same thing at the end of the game. Plus, he's our best player. He's our best back. You want your best player out there to start the game and finish it."
Jones gave Barber a seven-year, $45 million contract in 2008, before he became a full-time starter. Barber's production has dropped drastically in the last two seasons.
Barber averaged 4.8 yards per carry and rushed for a total of 24 touchdowns in 2006 and 2007. His average dropped to 3.7 yards per carry last season and is 4.4 this season, and he's rushed for a total of 11 touchdowns in the two seasons.
The Cowboys have two other capable backs in second-year players Felix Jones and Tashard Choice. Jones is averaging 6.4 yards per carry this season; Choice is averaging 5.6 yards per carry. They've combined for 127 carries, 25 fewer than Barber.
"I think any of those three backs can make a play," Jerry Jones said.