Reid, a staunch ally and former team-mate of ex-San Francisco 49ers quarterback Colin Kaepernick, had already accused the NFL of targeting him unfairly as retribution for his lawsuit against the league.
The 27-year-old, who joined Kaepernick in his take-a-knee protests during the playing of the US national anthem, filed a grievance in May after he remained an unsigned free agent.
That case remains active even though Reid was picked up by the Panthers in September after the 2018 season kicked off.
However, since joining the Panthers, Reid has drawn attention to frequent requests by independent doping control staff to submit to drug testing.
On Monday following the Panthers’ 12-9 loss to New Orleans, Reid was asked to undergo his seventh test of the season in 11 games.
Reid posted a picture of the doping order on Twitter, with the comment: “Number 7 … ‘random’.”
In comments to reporters, he later rejected any notion that he was being randomly selected for testing.
“I’ve been here 11 weeks, I’ve been drug tested seven times,” Reid said. “That has to be statistically impossible.
“I’m not a mathematician but there’s no way that’s random,” Reid added.
Under the collective bargaining agreement which sets out the rules for anti-doping protocols, the NFL and NFLPA are not involved in drug testing.
Drug tests are carried out by staff from an independent laboratory, which reportedly uses a computer to select names of players to be tested at random.
The same bargaining agreement also forbids publication of the identities of players chosen for testing, so it has not been possible to compare Reid’s test history with other players in the league.
Reid had earlier taken to the field wearing specially designed cleats which paid tribute “to the history of protest” while promoting Kaepernick’s “Know Your Rights” movement.
Kaepernick has not played in the NFL since the end of the 2016 season and has claimed he has been ignored by teams because of his history of protest.