Old English dreflian "to dribble or run at the nose, slobber," from Proto-Germanic *drab-, from PIE *dher- (1) "to make muddy, darken." Meaning "to speak nonsense" is mid-14c. Related: Driveling, drivelling.
early 14c., drevel "saliva, slaver," from drivel (v.). Meaning "idiotic speech or writing" is from 1852.