According to a source, the Cowboys have been negotiating with Ware on a reworked contract after the team let the seven-time Pro Bowler know last week they want him back in 2014, but not at the $12.25 million base salary.
The free-agent market opens at 3 p.m. CT Tuesday. Teams and agents have been able to talk about interest and parameters since Saturday, but players have not been able to talk directly to clubs or set up visits.
Whether the Cowboys release Ware or reach an agreement on a new contract, they will gain salary-cap space. By cutting Ware, the Cowboys would gain $7.4 million in cap space.
But the Cowboys do not need to cut Ware to get under the cap. After restructuring three deals (Tony Romo, Sean Lee, Orlando Scandrick), reducing one (Mackenzy Bernadeau) and releasing Phil Costa last week, the Cowboys are roughly $2 million under the cap.
While that is enough to sign a player to a reasonable deal, it is not enough to help fill multiple holes on a defense that finished last in the NFL in 2013. It would not be enough to keep last year's sack leader, Jason Hatcher, who is expected to receive heavy interest from teams in free agency.
Ware's camp would like a quick decision so that if he is cut, he would be able to hit the open market when teams have the most money to spend.
Ware's 117 career sacks are the most in franchise history, and he earned Pro Bowl honors from 2006 to 2012, but posted a career-low six sacks in 2013. Ware, who turns 32 in July, missed three games with a quadriceps strain and was bothered by a nerve issue in his elbow that required surgery after the season.
At the NFL scouting combine, executive vice president Stephen Jones said the Cowboys would be efficient spenders in free agency. In the past, they have set the markets on players -- like cornerback Brandon Carr, who received a five-year, $50 million deal in 2012 -- only to not get enough payoff on the deals.