NFL Network Insider Ian Rapoport reported on Wednesday that Bryant won't be signing with any team prior to the 2018 NFL Draft, which begins Thursday at AT&T Stadium in Arlington, Texas.
With teams focused on the draft, Rapoport also noted that Bryant could remain unemployed for another week or two.
Cowboys owner Jerry Jones publicly shut the door on the notion of Bryant returning to Dallas, with which the 29-year-old wideout has appeared in 113 games (99 starts) and amassed 7,459 total yards while registering a franchise-record 73 receiving touchdowns.
"We need to move on knowing that we don't have Dez," Jones said on Tuesday.
Bryant was cut loose in the face of a gaudy price tag -- he was scheduled to make $12.5 million in 2018 and count $16.5 million against salary cap -- as well as diminished returns from his previous seasons.
Jones and the Cowboys are expected to focus on improving their wideouts at the draft. Dallas holds the 19th overall pick of the draft, and Alabama wideout Calvin Ridley rests in that range in the most recent Big Board of NFLDraftScout.com senior analyst Rob Rang.
Ridley had 63 receptions for 967 yards and five touchdowns this past season for the Crimson Tide. He finished his career at Alabama with 224 receptions for 2,781 yards and 19 scores.
Dallas also brought in a pair of wide receivers via free agency in the offseason, signing Allen Hurns and Deonte Thompson.
"I think we recognize that we've got a hole to fill with Dez," Jones said. "We, actually, in general know right now that and have known that we probably won't have what we would call a pure X receiver to take the place of Dez.
"We know we won't have that because even if we draft one that is an X receiver he's not going to be, as a rookie, he's not going to come in here and give us that type of performance. You've got to assume that. And so, we certainly know that we've got a chance to pick a player, but not necessarily in the first round or even the second round, that will have the opportunity to be in the mix that gives that player a better chance to be playing next year and use a chance to have somebody who has some special skills, speed, that can help us out."
Bryant had a team-leading 69 receptions for 838 yards and six touchdowns with the Cowboys in 2017. He has gone a career-worst 23 regular-season games without a 100-yard performance.
Since signing a five-year, $70 million contract in 2015, Bryant has failed to record a 1,000-yard season or reel in more than eight touchdown receptions in a season.
Bryant was a touchdown machine in the first half of his career with the Cowboys, hauling in 41 scoring passes in a three-season span, capped by a career-high 16 in 2014. He was named a First-Team All-Pro selection that year.
During that spectacular run from 2012-14, Bryant also averaged 91 receptions and put up at least 1,233 receiving yards in each of those seasons.
The Baltimore Ravens were thought to be an early favorite to secure the services of the three-time Pro Bowl selection, but the team opted to sign restricted free agent Willie Snead from the New Orleans Saints.
Last week, Bovada gave the Ravens 3-to-1 odds of being the next team to sign Bryant. The Houston Texans were next with 4-to-1 odds, followed by the Green Bay Packers, Saints and Washington Redskins at 5-to-1.