That's no longer the case.
A person informed of the Cowboys' thinking has told NFL Media Insider Ian Rapoport that the team contacted Ware on Tuesday to pass along the message that they "definitely" want to keep him -- but not at his current salary of $13 million per year.
The sticking point is Ware's salary cap figure, which increases 98 percent from $8.1 million last season to $16 million this year.
The ball is now in Ware's court, armed with the knowledge that there will be no shortage of teams lining up to talk contract if the Cowboys call his bluff and cut him loose.
Although injuries led to a loss of effectiveness last season, Ware is still one of the NFL's difference-making pass rushers when healthy. Capable of playing linebacker in a 3-4 or defensive end in a 4-3, Ware has a strong case to become the league's most sought-after free agent if he makes it to the open market.
If Dallas loses Ware and defensive tackle Jason Hatcher, they are essentially starting from scratch on defense while the Philadelphia Eagles put a stranglehold on the NFC East.