DeMarcus Ware has given the Dallas Cowboys until 4 p.m. Tuesday to decide if the two sides have a future together.

With the NFL free agency signing period kicking off Tuesday, the Cowboys are on the record in asserting Ware will not remain on the roster at his current salary of $12.25 million. Still, the team remains interested in Ware and have proposed re-working the franchise's all-time sack leader's deal at a lower cost.

ESPN reports it's not known what salary the Cowboys have proposed for Ware, or if they plan to honor his request for a speedy resolution. The website adds the Cowboys might be able to gain leverage in the negotiations if they retain Ware beyond the early part of free agency, a time most teams use to broker new deals and complete the bulk of all offseason player transactions.

Ware had a career-low six sacks during an injury-riddled 2013-14 season, missing various games because of injury for the first time in his career. His loss was profoundly felt by the Cowboys, who fielded one of the league's worst defenses and in franchise history.

Ware's best season came in 2008-09, when he recorded a franchise-record 20 sacks and 84 tackles.