Strahan, Larry Allen, Jonathan Ogden and Warren Sapp are all first-year-eligible finalists. Parcells was a finalist last year.
The late George Young, former Giants general manager, did not make the cut as one of 27 semifinalists.
Strahan spent his entire 15-year career as a Giant, and is the team's all-time leader in games played (216) and sacks (141.5). The four-time first-team All-Pro set the NFL's single-season sacks record with 22.5 in 2001 to earn AP Defensive Player of the Year honors. The defensive end went to two Super Bowls, winning one in his final season.
Parcells guided the Giants to their first two Super Bowl victories during his tenure with the team from 1983 to '90. He went 77-49-1 in the regular season and 8-3 in the postseason. He also coached the Patriots, Jets and Cowboys, and became the first coach to lead four different teams into the playoffs.
To be elected to the Hall of Fame, Parcells and Strahan must receive a minimum of 80 percent of votes from the Hall's selection committee. Between four and seven new members will be selected Feb. 2, the day before the Super Bowl, in New Orleans.
The former coach and former team captain hope to join Morris "Red" Badgro, Roosevelt Brown, Harry Carson, Benny Friedman, Frank Gifford, Mel Hein, Sam Huff, Alphonse "Tuffy" Leemans, Tim Mara, Wellington Mara, Steve Owen, Andy Robustelli, Ken Strong, Fran Tarkenton, Lawrence Taylor, Y.A. Tittle, Emlen Tunnell and Arnie Weinmeister as Giants in the Hall of Fame.