Jones pointed out during his Friday appearance on KRLD-FM that Witten would have an extra week and a half without contact if he does not play in the Sept. 5 opener against the New York Giants.
"Obviously, we're here to win the ballgames, but not at the cost of the literal well-being of any individual," Jones said.
Witten suffered a lacerated spleen in the Cowboys' Aug. 13 preseason opener. He was cleared earlier this week for conditioning and on-field work, such as running routes and catching passes, but he has yet to be cleared for contact.
Witten is not expected to be re-evaluated until early next week, which means the chance of him playing against the Giants are "not good," a league source told ESPN NFL Insider Adam Schefter on Friday.
Jones said doctors called the seven-time Pro Bowler's injury a Grade 1 on a scale of 5 and that there have been no complications.
The only game Witten has missed in his nine-year career was because of a broken jaw suffered during his rookie season. He has played with other injuries such as broken ribs, but the Cowboys have made it clear that Witten's status for the season opener will be solely a medical decision.
"There's a judgment issue here, and there are some standards that might or might not apply to someone that is in the physical shape but do apply to someone that has the risk that a tight end, especially Jason Witten, would create to his spleen," Jones said.
"He'll be working out, I'm sure, today. You know Jason. Boy, I don't know on or off the field, football or nonfootball, that I've ever seen anybody as driven as Jason Witten. How he plays is how he is. And he won't take no for an answer."
Information from ESPN NFL Insider Adam Schefter was used in this report.