Ware, who will be 35 next season, is a free agent after playing the past three seasons with the Denver Broncos, where he won a Super Bowl ring in 2015.
Going back to Denver is an option, but so is a return to the Cowboys where he spent the first nine years of his career.
His representatives might have some informal talks with the Cowboys during the NFL Scouting Combine this week.
The only issue for Ware, regardless of where he signs, is his health.
He missed six games in 2016 and finished the season on injured reserve because of a ruptured disc in his back.
Ware is healthy after undergoing back surgery and believes he is ready to finish his career with a flourish, according to a source.
Ware is the Cowboys all-time leading sacker and a future inductee in the team’s hallowed Ring of Honor.
The question for the Cowboys is how much does he have left and how he fits in a Rod Marinelli’s defense that doesn’t generally make allowances for specialists.
But there is no doubt that a healthy Ware still fits a need for a Cowboys defense void of difference-making pass rushers.
Ware recorded four sacks last season in a part-time role, despite missing six games with injuries.
He has 11.5 sacks over the past two seasons.
Ware also ranked higher among edge defenders in 2016, per Pro Football Focus, than any current Cowboys player, despite his limitations.