Hinduism in Greece?

While reading the passage in Phaedo that talked about the immorality of the soul, the thought that immediately came to my mind was the religon Hinduism and reincarnation.  The discusion of the soul descendng to death and back into a differnt body highly resembles the process of reincarnation where a human soul returns to earth in another body.  In fact, Socrates seems to be describng the main process of reincarnation when he discussed the idea of good or bad works determining whether the soul inhabits the body of a certain animal.  My question is whether Socrates was knowingly referring to th religion of hinduism or if he came to this idea himself.