The NFL Players Association filed the grievance on behalf of Reid after Bengals owner Mike Brown reportedly asked if Reid would continue kneeling during the national anthem.
Reid was brought in by the Bengals for a free-agent visit at the time but was not signed. The grievance argued that the Bengals negotiated in bad faith because the team had no intention to sign Reid if he said he would continue to kneel -- despite the fact that standing for the national anthem is not mandated in the collective bargaining agreement.
The arbitrator ruled the Bengals were within their rights to ask if Reid would continue to kneel. Reid began kneeling during the anthem during the 2016 season when he was with the San Francisco 49ers as a way to support Colin Kaepernick and draw attention to issues of social injustice.
"Arbitrator Shyam Das issued a decision yesterday siding with management and denying Eric Reid's claim against the Cincinnati Bengals. We are disappointed in this decision, especially since the arbitrator affirms the facts which our filing was based upon and provides no in-depth analysis of why management can engage in behavior that violates fair hiring practices," the NFLPA said in a statement Tuesday.
"Despite this decision, we are thrilled that Eric Reid is back with an NFL club doing the job he loves and our hope is that Colin Kaepernick follows him back to the playing field soon. We will review the decision more carefully with Eric and his lawyers to consider our next steps."
Reid remained a free agent until he was signed by the Carolina Panthers in September and has continued to kneel during the national anthem. Kaepernick, who was the first player to begin kneeling during the anthem, remains unsigned and hasn't played since the 2016 season.
Reid and Jenkins have been feuding since Jenkins, the co-founder of the Players Coalition, stopped raising his fist during the anthem after the NFL announced it would donate $100 million to causes considered important to the coalition.
"He co-opted with the movement that was started by Colin to get his organization started. It was cowardly. He sold us out," Reid told reporters.
Reid and several other players withdrew from the coalition in November 2017, and he has since called it an "NFL-funded subversion group."
The Bengals have not commented on the grievance ruling.
Reid still has a grievance pending against the NFL. In May, Reid and his attorney, Mark Geragos, filed the grievance, alleging that team owners and the league, influenced by President Donald Trump, colluded to prevent his employment because of his protests. Kaepernick filed a similar grievance and an arbitrator recently sent it to trial, denying the league's request to have it thrown out.