Ware, who played in 134 consecutive games prior to suffering the injury, should be ready for Sunday night's game against the New Orleans Saints, Jones said.
During his Tuesday morning radio show on KRLD-FM, Jones gave a long-winded answer regarding Ware's playing status before finally saying, "I think he's ready."
Jones, in his answer, said the Cowboys didn't want to rush Ware back to the field because out of fear he would re-injure himself.
If that occurred, the Cowboys would be without their best defensive player. Ware has four sacks and 16 quarterback pressures this season.
"I'm going to call it, made an investment into the future and the latter part of the season to be conservative on how fast we put him out there," Jones said.
Austin said it's up to the trainers to decide when he returns. Claiborne said he's been running sprints but hasn't been cleared to practice.