Jones, who made his comments in an interview with 105.3 The Fan in Dallas, didn't disclose the exact location where the running back is training.
NFL Network first reported the news of Elliott's plans.
"Actually, I give Zeke credit. This was his idea. He's wanting to really go to work and not have distractions while he's not able to play the game. He felt the best way to do that was to get away from this environment ... and really work to get himself in the best possible shape," Jones said.
Jones said Elliott went over his plans with the team's coaches and strength and conditioning staff, who were comfortable with what they heard.
Cowboys owner and general manager Jerry Jones, Stephen's father, said Sunday night that he also believed Elliott had a good plan for his time away from the team.
Stephen Jones noted that the Cowboys aren't permitted to have contact with Elliott during his suspension but was hopeful that the running back will be able to stay in playing shape.
"Certainly it's not easy when you're not in a competitive environment, but it sounds like he has a good plan and hopefully one he'll pull off," he said.
Elliott, 22, was suspended by commissioner Roger Goodell in August after the league concluded following a yearlong investigation that he had several physical confrontations in the summer of 2016 in Ohio with his girlfriend at the time. The NFL players' union sued on Elliott's behalf.
He was able to play in the first eight games through a number of legal decisions, but he lost a temporary administrative stay that kept him on the field in last week's victory over the Kansas City Chiefs.
The Cowboys missed Elliott in Sunday's 27-7 loss to the Atlanta Falcons, as the team rushed for 107 yards on 21 carries. Alfred Morris led the Cowboys with 53 yards on 11 carries but had just 8 yards on six first-half carries. Elliott had 783 rushing yards in the first eight games of the season, with four straight games of more than 90 yards on the ground.
He will miss at least the next four games, pending a Dec. 1 hearing, and he is likely to miss the next six.
"He'll be a better person from this and a better player for us when this is all said and done. It will be a life lesson for him and hopefully he'll come back and take the next chapter," Stephen Jones said.
ESPN's Todd Archer contributed to this report.