Kelly has been the Bears' assistant director of player personnel for the last two years after joining the organization as its pro scouting director in 2015.
He and Jets coach Adam Gase have worked together previously for seven seasons. Kelly was in Denver for eight years in various roles from 2007-14, including assistant director of pro personnel his last three seasons with the Broncos. Gase was Denver's wide receivers coach, quarterbacks coach and then offensive coordinator from 2009-14. Both Kelly and Gase went to Chicago in 2015.
The Jets have also interviewed Philadelphia Eagles vice president of player personnel Joe Douglas; New Orleans Saints director of pro scouting Terry Fontenot and Seattle Seahawks co-director of player personnel Scott Fitterer.
Jets chairman and CEO Christopher Johnson fired GM Mike Maccagnan on May 15 after four seasons. Gase has had an active role in the interview process to find Maccagnan's replacement.