Executive vice president Stephen Jones spoke to ESPN's Todd Archer on Wednesday and said all three playmakers have earned the right to seek a max contract. However, that would hinder the team's ability to keep all its stars in the future and fill out the rest of the roster.
The Cowboys signed pass-rusher DeMarcus Lawrence to a five-year, $105-million extension in April.
"As I told DeMarcus Lawrence, and I'll tell all three of these guys: I'd love for you to max out and give you exactly what you want, because y'all have worked hard and you deserve to have a big contract. But if we want to put together the type of team we want to have with the Cowboys ..." Jones said.
"That's not their job. It's not their job to manage the cap; I understand that. But it is my job and (owner Jerry Jones') job, so they will understand why we're negotiating hard to make the very best deal we can. Because the money, if we can talk them into not maxing out - doing well, but not maxed - then that allows us to have other good football players around them."
Although the Cowboys intend to offer Elliott an extension, the franchise is focusing its immediate attention on Cooper and Prescott, who are entering the final year of their current contracts.
"Zeke, as we all know, he's such an important player to this organization. He's a guy that we want to have long term," Jones said. "The only reason you say, 'Well, maybe he's not at the front, front (of the line),' is because he's got this year, then he's got another year at his tender."