McShay told ESPN's Rich Cimini that Jets general manager Joe Douglas is considering him among multiple options for an unspecified front-office role.
McShay and Douglas know each other from their college days as teammates on the University of Richmond's football squad.
The Jets announced Friday they agreed to terms with Douglas to become their new general manager after Mike Maccagnan was fired on May 15.
Douglas spent the previous three years as vice president of player personnel with the Philadelphia Eagles. He won a Super Bowl with the team during the 2017 season.
As NFL teams continue to search for an edge on the field, media analysts have received more interest. The Oakland Raiders hired Mike Mayock away from NFL Network to serve as their general manager.
Daniel Jeremiah has also received serious consideration from the Jets for a front-office role, per ESPN's Adam Schefter.
McShay has been a draft analyst at ESPN since 2006. He also serves as a sideline reporter throughout the college football season. The 42-year-old was a walk-on quarterback at Richmond from 1995 to 1997 and served as an undergraduate assistant on the coaching staff.