The 15 finalists were announced on Thursday, and the inductees will be named on Feb. 1 -- the eve of the Super Bowl.
Greene, who played 15 years for the Rams, Steelers, Panthers and 49ers, ranks third on the all-time sack list with 160. Nos. 1, 2 and 4 (Bruce Smith, Reggie White and Chris Doleman, respectively) all have been inducted into the Hall of Fame. No. 5 Michael Strahan also is a finalist this year.
"It'd be cool; It'd be neat," Greene said on Wednesday. "I don't want to get overly up about it or down about it. My focus right now is evaluating my young men and the season they've had. What can I do to be a better coach for them moving forward."