Quinn reportedly interviewed for the job earlier this month and is considered the favorite. However, the Jets cannot offer Quinn the job until the Seahawks are eliminated from the playoffs.
Seattle beat the Carolina Panthers on Saturday night to advance to the NFC Championship game next weekend.
According to ESPN, Quinn will likely receive multiple head coach offers and is receiving interest from the Chicago Bears.
Arizona Cardinals defensive coordinator Todd Bowles and Seahawks assistant head coach/offensive line coach Tom Cable are also considered among New York's leading candidates.
Quinn, 44, has been the Seahawks' defensive coordinator the past two seasons and spent two years on the team's staff in 2009 and 2010 as well, with a stint as Florida's defensive coordinator in between.
Seattle has finished No. 1 in total defense in each of Quinn's two seasons, allowing 273.6 and 267.1 yards per game. The Seahawks' defensive prowess was a key factor in the team's Super Bowl win last season.
The Jets fired head coach Rex Ryan and general manager John Idzik in December following a 4-12 season. New York is reportedly expected to hire Houston Texans director of college scouting Mike Maccagnan as its new GM, and ESPN reports that Maccagnan would have gone to Seattle to pursue Quinn had the Seahawks lost.
- Molly Geary