The sixth pick in the 2012 draft will not participate in offseason workouts and likely won't be ready for the start of training camp because of the torn patellar tendon in his left knee that kept him out of 12 games last season.
A story on the team's website Monday revealed the expected move. Morris would have been guaranteed about $11 million in 2016 had the Cowboys picked up the option.
Dallas used its first-round pick in last week's draft, No. 27 overall, on cornerback Byron Jones from Connecticut.
Claiborne started 15 games as a rookie in 2012, when he had 43 tackles, one interception and eight passes defended. He played 10 games, starting seven, in 2013 when he had 24 tackles and an interception while dealing with a hamstring issue.
The other Cowboys first-round picks from 2010-14 have all made the Pro Bowl: receiver Dez Bryant and offensive linemen Tyron Smith, Travis Frederick and Zack Martin.
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