Suggs, who missed practice Monday and Tuesday because of a neck injury, is listed as day-to-day. The two-year veteran was a fourth-round draft pick by the Browns in 2003 out of Virginia Tech.
He has 289 yards on 56 carries in two seasons and was the likely starter for the Browns in the opener.
In case he is not available, former starter William Green could be his replacement, with James Jackson in reserve.
"It's not up to me," Suggs told the Cleveland Plain Dealer in response to a question about whether he would play.
"He's day-to-day right now," Coach Butch Davis told the newspaper Tuesday. "The decision rests, as they always do, with our doctors."