Jones also said the franchise is "sold" on Prescott. The fourth round pick in the 2016 NFL Draft is entering the final year of his rookie contract. Prescott, 25, has a 32-16 record as a starter.
He has completed 66.1 percent of his passes for 10,876 yards, 67 scores and 25 touchdowns in 48 starts since being drafted out of Mississippi State.
"We are sold on Dak," Jones told the Rich Eisen Show on Monday. "We do want to have him for the long term. We think he is worthy of investing in for the long term. He is going into his fourth year in the NFL. When you look at the snaps he has had, the situations he has been in and how he got here and you see how he has performed ... we see real upside in Dak."
"You don't have it all yet. We love the way he logically progresses through a game. You see when the going gets tough, when he's got to come from behind, when he turns it loose a little bit. You see him make those plays. All of these things embolden me to make a deal with him that puts him here for the long term."
The Cowboys have been negotiating with Prescott and wide receiver Amari Cooper this off-season. Cooper is also entering the final year of his rookie pact. The No. 4 overall pick in the 2015 NFL Draft joined the Cowboys in October in a trade from the Oakland Raiders.
Cooper is making $13.9 million this season, while Prescott is on the books for just $2.1 million in 2019. Cooper is likely to see an offer paying him at least $16 million annually, while Prescott could cash in for close to $30 million annually.