Odom wasn't available Friday during the team's open locker room period. Coach Marvin Lewis said there was no change in the status of the appeal.
"It's something that's been ongoing for a while," Lewis said. "Obviously a couple guys played last night [in the Saints' 14-9 win over the Vikings] who have been through that who are still playing."
Although he didn't meet with the media on Friday, Odom acknowledged on his Twitter account that he tested positive for a banned substance. He denied reports that his four-game suspension is for using performance-enhancing drugs.
"Yes, I tested positive for a banned substance but it wasn't steroids or [performance-enhancing drugs]," Odom tweeted. "More details to come but for now it's a league issue that's under appeal. Just know that I would never cheat to gain an edge in this game that I love."
Two years ago, Bengals linebacker Darryl Blackstock got a four-game suspension for using a performance-enhancing substance. Blackstock said one of his nutritional supplements included an ingredient banned by the league.
The NFL could deny Odom's appeal and force him to miss four games, or reduce the penalty. Losing Odom would be a significant setback to Cincinnati's pass rush.
The 28-year-old lineman led the team with eight sacks when he tore his right Achilles tendon only six games into last season. He still led the team in sacks for the season despite his injury.
He has fully recovered from the injury. Odom missed time during training camp because of an illness and a sore knee, but is expected to rejuvenate a defensive line that made pressuring the quarterback a priority this season.
The Bengals signed Odom as a free agent from Tennessee in 2008, their major offseason acquisition to help the defense. A foot injury limited him to eight starts and three sacks in his first season with the Bengals.
Last season, he emerged as one of the NFL's best at getting to the passer. He has seven sacks in the first two games, an NFL record. He was tied for the league lead when he tore his Achilles Oct. 18.