League sources indicated to ESPN.com there is "growing uncertainty inside and outside the organization" as to whether Rose will return.
Rose has missed 11 of 18 games this season, including the previous seven.
"Per Wojnarowski, a Cavaliers source said, "[Rose is] exhausted of being hurt, and it's taking a toll on him mentally".
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When Derrick Rose went AWOL from the Knicks last season for what he called a family issue, rumors swirled that he was contemplating retirement.
The Cavs announced that Rose would be out for at least the next two weeks because of the ankle one week ago, and Rose then also was put in a walking boot. He missed Cleveland's next four games, but returned October 29 for a loss to the Knicks. "So I'll wear this, for I don't know how long, to see how it helps". In 2012, he suffered a torn ACL in his left knee during the playoffs causing him to miss the 2012-13 season. He's averaging 14.3 points per game in his first season with Cleveland.