Williams isn't believed to have any significant ligament damage to the knee, according to the newspaper.
Williams -- along with teammate and fellow defensive tackle Pat Williams -- tested positive for a banned diuretic in 2008. The players have been fighting their suspensions since.
The Minnesota Court of Appeals ruled Tuesday in Minneapolis that it won't permanently block the NFL from suspending the Williamses for violating the league's anti-doping policy.
Barring another appeal, the ruling appears to clear the way for the NFL to suspend the players. The players could appeal this latest decision to the state Supreme Court.
The Associated Press contributed to this report.