According to ESPN.com's Tony Grossi, the 24-year-old wideout will learn within 60 days if he is eligible to return to the league as a member of the Browns.
On Thursday, Browns executive vice president Sashi Brown said Gordon "could be back" with the team if he's reinstated, adding "we'd sit down with Josh and see where he is," per Mary Kay Cabot of the Cleveland Plain Dealer.
While Gordon is an immensely talented player, his off-field issues have limited him to just five games over the past two seasons.
Per ESPN.com's Jeremy Fowler, the 2013 Pro Bowler and All-Pro selection has been suspended three times for violating the NFL's substance abuse policy. The most recent suspension began in February 2015 for alcohol, and he previously served a suspension after testing positive for marijuana.
The 2012 NFL supplemental draft second-round pick has proved to be a dominant receiver in 35 career NFL games, and that was on full display in 2013.
Gordon caught 87 passes for 1,646 yards and nine touchdowns in 14 games that season, and he seemed well on his way to establishing himself as one of the league's elite pass-catchers for a long time to come.
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Substance abuse problems derailed that, but another chance could be on the horizon.
The Browns haven't revealed their intentions for Gordon should he get reinstated, but new head coach Hue Jackson recently discussed his plans regarding the polarizing star, according to Mary Kay Cabot of Cleveland.com: "I'm anxious to evaluate him like we're going to evaluate every player on the roster and see if they are the right fit for the Cleveland Browns. And I think that's what we have to do every player from Josh Gordon to the last player on the roster."
Gordon is still under contract for one more year at the affordable price of just over $1 million, per Spotrac.
Adding him to the mix would be a huge boost for an offense that saw wide receiver Travis Benjamin and tight end Gary Barnidge blossom into quality targets in 2015.
It isn't yet clear what Cleveland's quarterback situation will look like in 2016, but with Johnny Manziel seemingly on the outs, a rookie such as California's Jared Goff or Memphis' Paxton Lynch could be brought in with the No. 2 overall pick in the draft.
A focused Gordon could go a long way toward helping a young signal-caller develop, but Cleveland remains at the NFL's mercy.
Even if the Browns decide against welcoming Gordon back into the fold due to the headaches he has caused in recent years, there is little doubt that someone will take a chance on the troubled receiver due to what he is capable of on the field.
Follow @MikeChiari on Twitter.