Terry Bradshaw doubts Antonio Brown will ever see another snap in the NFL ... telling TMZ Sports straight-up, "I wouldn't sign him."
"He's erratic," Bradshaw told us in NYC ... "His behavior makes me nervous. I don't know what's wrong with him. It makes no sense."
AB added another chapter to one of the most bizarre NFL stories ever on Thursday ... quitting the league in a profanity-laced social media rant, before eventually backtracking.
Bradshaw agrees the 31-year-old WR is crazy talented, but the off-the-field issues could be too big of a hurdle for him to overcome.