He was among the first players to join then-49ers quarterback Colin Kaepernick in kneeling during the national anthem to protest police brutality and racial injustice two years ago.
While Kaepernick did not have a team last season, Reid continued to kneel as a member of the 49ers.
That has been assumed to have a role in his remaining unsigned at this point in the offseason, although he has also had some injury issues over the past two seasons.
Reid told reporters in late March he does not plan to kneel this season but will continue to be politically active.
"I'm not going to say that I'm going to stop being active because I won't," said Reid, who spoke with reporters Thursday after watching his younger brother, safety Justin Reid, participate in Stanford's Pro Day. "I'm just going to consider different ways to be active. Different ways to bring awareness to the issues of this country. To improve the issues happening in this country.
"I don't think it will be in the form of protesting during the anthem. … I think we're going to take a different approach to how to be active."
The Bengals have shown interest in adding a veteran safety since the start of free agency when they met with former Ohio State and Northmont High School standout Kurt Coleman, who eventually signed with the New Orleans Saints instead.
Reid was a highly regarded prospect coming out of LSU in 2013, but he was drafted 18th, three spots before the Bengals chose Notre Dame tight end Tyler Eifert.