The deals would reportedly put each player among the top five highest-paid players at their respective positions.
Slater noted Dallas is willing to close the deal with each player, though the team is also prepared to have the stars play on "prove it" contracts in 2019 if the two sides can't reach an agreement.
Both Prescott and Cooper are entering the final years of their respective rookie contracts, while Elliott is under club control for two more seasons.
Taken fourth overall in 2016, Elliott has led the league in rushing in two of his first three seasons. He has led the league in rushing yards per game in all three seasons, piling up 101.2 yards per contest for his career.
Elliott has opted to hold out this offseason as he seeks an extension. Hall of Famer Eric Dickerson revealed on FS1's Undisputed With Skip and Shannon on Monday that Elliott's agent told him it's "possible" the 24-year-old running back will sit out regular-season games if a new deal is not reached:
A fourth-round pick in 2016, Prescott has led the Cowboys to a winning record in each of his first three seasons, taking a pair of NFC East titles in the process. The two-time Pro Bowler is coming off a season in which he completed 67.7 percent of his passes for 3,885 yards, 22 touchdowns and eight interceptions.
The 26-year-old signal-caller previously hinted back in February that he would not take a hometown discount on an extension, telling Jori Epstein of USA Today that Dallas "knows how to pay what's deserved."
It's worth noting Prescott has been one of the best bargains in the league since he was drafted:
Cooper, meanwhile, quickly proved how valuable he was to the team after being acquired in a midseason trade last year. The Cowboys were 3-4 prior to acquiring Cooper and wound up going 7-2 the rest of the en route to a division title.
Dallas also recorded a playoff victory for just the third time in two decades before falling to the eventual NFC champion Los Angeles Rams in the divisional round.
Cooper had 53 receptions for 725 yards and six touchdowns in nine games for Dallas. After also having 280 yards in six appearances for the Oakland Raiders, the two-time Pro Bowler topped the 1,000-yard mark for the third time in his career.
Cowboys owner Jerry Jones recently revealed, per NFL.com's Adam Maya, that he has no concern about getting deals done with each star, saying "it'll happen." For now, though, the team will have to continue to try to find common ground in negotiations.