Smith said $3.1 million comes from the $1.55 million base salary that Bryant had been scheduled to earn this season in Cincinnati and the $1.55 million roster bonus that was due to him.
The Bengals have seven days to respond to the grievance and decide whether they want to settle. If they don't, the case would go to the NFL Players Association and NFL management council for a ruling.
Cincinnati cut Bryant last month, after paying him nearly $8 million in guaranteed money this offseason. Bryant battled knee injuries and did not practice with Cincinnati this summer.
Smith said Bryant intends to resume his NFL career but is a month away from being ready to play.
Adam Schefter is an NFL reporter for ESPN Insider.