Quinn reportedly interviewed for the job earlier this month.
According to the Post, his interview and those of Arizona Cardinals defensive coordinator Todd Bowles and Seahawks assistant head coach/offensive line coach Tom Cable have been the most impressive so far. Bowles and Cable have become the other front-runners for the head coaching job behind Quinn.
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 Post also reported that Houston Texans director of college scouting Mike Maccagnan has emerged as the favorite to land New York's vacant general manager job after becoming the only candidate to interview for a second time on Friday.
Maccagnan has been in his role with the Texans since 2011.
The Jets fired coach Rex Ryan and general manager John Idzik after the season ended. New York went 4-12 this season, recording its fewest wins since it also went 4-12 in 2007, and missed the playoffs for the fourth consecutive season.
- Ben Estes