Old English dreflian "to dribble or run at the nose, slobber," from Proto-Germanic *drablojanan, from PIE *dher- "to make muddy." 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.