Per CBS Sports' Jason La Canfora, the Cowboys have made "no progress" with Prescott or Cooper, and "no talks are anticipated" until after the 2019 season ends.
La Canfora reported in October the Cowboys had plans on using the franchise tag to retain cornerback Byron Jones, but Prescott's demands were "going beyond" the team's offer, and it might be forced to use the one-year tender on him.
Jones "looks increasingly likely he will be elsewhere" next season, per La Canfora. The 27-year-old made his first Pro Bowl appearance last season. He's tied for second on the team with five passes defensed this season.
Prescott could reset the quarterback market when he signs a new deal, with CBS Sports' Joel Corry listing Jared Goff's four-year extension with $110 million guaranteed from the Los Angeles Rams as the benchmark.
La Canfora noted the only way Cooper and Prescott are likely to be with the Cowboys next season is if they can use the franchise tag on Cooper without the risk of losing Prescott.
Spotrac estimates the Cowboys will have $89.1 million to spend before factoring in potential extensions or franchise tenders for Prescott, Cooper or Jones.
Dallas owner Jerry Jones has been aggressive in giving long-term deals to core players in recent years, including Ezekiel Elliott, Jaylon Smith, Zack Martin and DeMarcus Lawrence.
That strategy has paid off with three division titles in the past five years but could leave the Cowboys scrambling to create more cap space in an attempt to keep all of their key players around for at least one more year.