Karney, 29, has one year left on a three-year, $3.5 million contract that he signed as a free agent in March 2009. He would be due $1.1 million in base salary next season.
The veteran back was inactive in Weeks 12 through 15, and new offensive coordinator Josh McDaniels' scheme doesn't provide much work for a fullback.
"You know in this league, it's no secret, it all starts with the quarterback," Karney told the newspaper. "Every team is quarterback-driven, and they have a great young talent in Sam, and they need to build around that. That's the business. It's tough for me in my position, but I'm not going to kick or scream or yell. What can you do? You've just got to take the experiences and what you've learned from 'em and move on."