Elliott had a sensational rookie season in 2016 when he was the NFL's rushing champ with 1,631 yards and almost topped 1,000 yards last season despite playing in just 10 games.
Elliott missed six games for violating the league's personal conduct policy, stemming from domestic violence allegations in July 2016. Elliott had a lengthy legal battle to fight the suspension but eventually accepted it.
Keeping Elliott available and eligible ranks as one of the top priorities for the Cowboys, but Jones said the organization "can only do so much."
"These are grown men," Jones said from the NFL Scouting Combine. "I have a lot of confidence that Zeke has learned a lot. Hopefully he has.
"Because if he has and he changes his behavior and he's able to stay on the field, we all know he can be one of the greatest to ever play the game, if he takes care of himself and takes care of his business off the field.
"I think Zeke wants that. He's a competitor. I think he wants to be one of the best.
"He certainly knows that he's got to take care of business, too. We've had great players that have had to do better before. Michael (Irvin) will tell you that he had to learn valuable lessons. But he turned out to be a Hall of Famer.
"I think if Zeke will pay attention and do the right things off the field and be responsible then he can certainly have an amazing career."
Elliott appears to be headed on the right track. He hasn't made headlines for the wrong reasons since his suspension after doing so a head-scratching number of times during his rookie year.