The Miami Dolphins dismissed Gase after going 7-9 during the 2018 regular season.
New York conducted interviews with newly-hired Arizona Cardinals head coach Kliff Kingsbury, former Green Bay Packers head coach Mike McCarthy, and former Detroit Lions head coach Jim Caldwell for the position. Baylor head coach Matt Rhule was also reportedly linked to the job.
Gase went 23-25 during his three seasons as head coach of the Dolphins, beating the Jets in five of their six meetings.
His previous experience includes a brief stint as the offensive coordinator of the Chicago Bears in 2014, as well as the Denver Broncos' offensive coordinator in 2013 when Peyton Manning threw a record-setting 55 passing touchdowns in a single season.
Dowell Loggains is expected to be named as an offensive assistant with the Jets, sources told ESPN's Jeff Darlington. Loggains was the Dolphins' offensive coordinator during the 2018 season.
Former Broncos head coach Vance Joseph is a strong possibility for Gase's defensive coordinator, according to NFL.com's Ian Rapoport.
The Jets fired Todd Bowles on Dec. 30 after going 24-40 in four campaigns at the helm. The team hasn't had a winning season since 2015.
The Cincinnati Bengals and the Dolphins remain the only teams yet to name their head coach for the 2019 season.