Aikman was a Super Bowl quarterback and MVP with the Dallas Cowboys. White was a two-time NFL Defensive Player of the Year during his career with the Green Bay Packers and Philadelphia Eagles.
Other modern-era finalists include wide receivers Art Monk and Michael Irvin; linebackers Harry Carson and Derrick Thomas; defensive ends L.C. Greenwood and Claude Humphrey; and offensive linemen Russ Grimm, Bob Kuechenberg and Gary Zimmerman.
The senior committee's finalists are offensive tackle Rayfield Wright and coach/television analyst John Madden.
The Hall of Fame's Board of Selectors will meet in Detroit on Feb. 4 -- the day before Super Bowl XL -- to determine this year's Canton inductees.
The 15 finalists were trimmed from an original list of 112 preliminary nominees. That group was reduced to 25 semifinalists.