John Clayton of 710 ESPN reported the Seahawks plan to pursue Gordon, who would be be an unrestricted free agent. Gordon was suspended indefinitely in December for violating the NFL's policy on performance-enhancing drugs and substances of abuse.
The former Pro Bowler applied for reinstatement in June.
Gordon spent a little over a month with the Seahawks last season after being waived by the New England Patriots, recording seven receptions for 139 yards in five games.
The 2013 NFL leader in receiving yards, Gordon has been limited to just 33 games over the last six seasons after violations of the league's substance abuse policy. He missed the entire 2015 and 2016 seasons while suspended and has not made it through a full NFL season without a substance-related suspension since 2012.
Adam Kenner, Gordon's attorney, said his positive test last season was the result of a relapse after the death of his brother.
"Josh had a lapse because of his brother's death," Kenner told Tom Pelissero of NFL Network. "But since that time, he has realized how important it is for him to take the right steps, do what's proper and understand how to manage these issues. He's installed the right team around him to make sure he's on the right path. He understands he’s been given every chance. He looks forward to making the most of this."