Ryan is currently the defensive coordinator of the New Orleans Saints and helped turn their defense from the worst in the league in 2012 to one of the best in 2013.
"You tell me one other reason why he doesn't have a [head-coaching job] right now with the kind of job he did," he told reporters.
"Maybe that's it. I told him, 'Dude, how about you go get a haircut? It makes no difference.' I said, 'You can wear the Fu Manchu if you're bald.'
"I can't explain it. Is it the hair? I don't know. I'm trying to get him to get a haircut. Hopefully, this is one of the things that motivates him to do so."
Rex has been in charge of the Jets since the 2009 season.