Oakland general manager Reggie McKenzie told Vic Tafur of the San Francisco Chronicle that Smith has applied for reinstatement.
The pass rusher's one-year suspension for violating the NFL Policy and Program for Substances of Abuse expires on Nov. 17, meaning Smith could suit up this season pending a positive meeting with Commissioner Roger Goodell.
"'Aldon is doing well," McKenzie said Wednesday night, per Tafur. "That situation is going to be totally up to the league because he's been in the program and they've monitored him. It's up to Goodell to say yah, nay or when. And he could say no to everything ... that part is out of our hands."
Said McKenzie: "The league will take everything into consideration and Aldon will have to meet with Goodell at some point."
Smith's once-promising pro career has been sidetracked by a rash of off-the-field issues. The 27-year-old pass rusher has been arrested three times for DUI and entered a treatment center in July.