The closest thing we have to a response are literary depictions of the gymnosophists ("naked wise man"), which basically translates to "naked wise men". From what descriptions we have it is difficult to know whether these are Jain, Buddhist, Ajivika or Vedic Hindu. In fact it is probably best to think of these as highly fluid categories at the time, and so these are some sort of "generic" sramana (sort of personal ascetic) monks. They don't seem to have had a direct influence on classical philosophy but many observers were highly impressed by their devotion to spiritual pursuits. One in particular, Kalanos, traveled with Alexander the Great, and at the end of his life chose self immolation over slowly wasting away.

That being said, I personally believe that Buddhism was highly influential in the development of Western monasticism, but there isn't really any direct evidence.