Old English dreflian "to slaver, slobber, run at the nose," from Proto-Germanic *drab-, perhaps from a PIE *dher- (1) "to make muddy, darken." Transferred meaning "to speak nonsense" is mid-14c., driveling being characteristic of children, idiots, and dotards. Related: Driveling, drivelling.
early 14c., drevel "saliva, slaver," from drivel (v.). Meaning "senseless twaddle, idiotic speech or writing" is by 1852.