Prescott, who is entering the final year on his rookie deal, is expected to make just $2million this upcoming season and has made it clear he wants a new contract that represents his value to the team.
The Cowboys face a tricky off-season in re-negotiating contracts as they have several stars looking to extend their current deals on improved terms.
Dallas recently secured the services of defensive end DeMarcus Lawrence, after offering him a $105m deal over five years, with $65m guaranteed.
However, they still have franchise quarterback Prescott, potential Hall of Famer running back Ezekiel Elliott and star wide receiver Amari Cooper still waiting to see what is offered.
Peter Schrager, a co-host on Good Morning Football on the NFL Network, believes Prescott will be next ahead of Elliott and Cooper.
“I think Dak Prescot’s next,” Schrager said on GMFB.
“I feel like you got to get the quarterback done.
“I feel like you don’t want to go into the season, of the final year of a contract, being paid $600,000 contract as quarterback to America’s team, who won a playoff game last year and all his team-mates love and believe in him.
“Take care of Dak.
“I am not saying he is going to break any records and make Aaron Rodgers money, but give him what is reasonable.
“Give him the money what a franchise quarterback deserves and lets roll with this generation of Cowboys.
“Take care of your quarterback and funnel it down from there.”
If a deal is agreed with Prescott, the size of his payday could affect how much is left to offer Elliot.
The running back still has two years remaining on his four-year deal, which guaranteed him $24.9m and included a $16.3m signing bonus, but Cowboys owner Jerry Jones has spoken about not wanting to risk losing an elite running back in the near future.
However, the Cowboys do risk upsetting their quarterback if the two sides can’t agree on what he is worth.
Earlier in the week Cowboys executive vice president Stephen Jones said Prescott will need to have a “team-friendly” deal so Dallas can build a competitive side around him.
Last season Prescott led the Cowboys to the Divisional Round of the playoffs, where they just came up short against the Los Angeles Rams and lost 30-22.
During the 2018 regular season Prescott threw for a career-high 3,885 yards, 22 touchdowns and eight interceptions and finished the year with a passer rating of 96.9.