Prescott, 25, completed 67.7 percent of his throws for 3,885 yards, 22 touchdowns and eight interceptions in 16 starts last season. The two-time Pro Bowl selection is entering his fourth season after being selected by Dallas in the fourth round of the 2016 NFL Draft.
The Cowboys quarterback is set to make $2.1 million in the final year of his rookie deal.
Cooper, 24, was the No. 4 overall pick in the 2015 NFL Draft. He played for the Raiders until being traded to the Cowboys in October in exchange for a first round pick in the 2019 NFL Draft. He is set to make $13.9 million in the final year of his rookie pact.
Cooper struggled through his first six games with the Raiders last season. He had 53 catches for 725 yards and six scores in nine games for the Cowboys.
"Yeah, we're always open to looking at things," Jones said. "Certainly if there are opportunities there that make sense, then we'll progress. I think pretty much everybody's on it pretty good that there's some pretty active discussions now with Dak and Amari, but it doesn't mean that some can't pick up in short order with other players that we have on our roster that we certainly want to keep here in Dallas and have them remain Cowboys in the future."
The Cowboys have also had early talks with the agents for running back Ezekiel Elliott and cornerback Byron Jones.
Seattle Seahawks quarterback Russell Wilson signed a record four-year, $140 million contract extension Tuesday, but you shouldn't expect a similar contract for Prescott. Jones pointed out that Aaron Rodgers and Wilson received their contracts as Super Bowl champions, while Prescott has yet to reach the NFL's biggest stage in his young career.
Jones mentioned that Prescott's new deal needs to be "team friendly" so that the Cowboys can maintain a competitive roster overall.
Elliott is one of the league's best running backs. He is due $7.94 million in the final year of his rookie contract. Jones -- who made his first Pro Bowl in 2018 -- is due $6.2 million in the final year of his rookie deal.
The Cowboys had their first day of off-season workouts on Monday and begin mandatory minicamp on June 11.