The committee discussed Parcells for close to an hour, Rick Gosselin of Sports Illustrated told NFL Network.
Charles Haley, a member of the Cowboys from 1992-96, was among the final 10 candidates.
Allen played for Dallas from 1994-2005 and San Francisco from 2006-07. He was named a first-team All-Pro seven straight years.
Parcells coached the Cowboys from 2003-06. Took four teams to the playoffs, winning two Super Bowls with the New York Giants.
The class also includes receiver Cris Carter, defensive tackle Curley Culp, tackle Jonathan Ogden, linebacker Dave Robinson and defensive tackle Warren Sapp.
Stay tuned to ESPN.com for continuing coverage.
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