Theosis, deification, partaking in the Divine Nature, call it what you will--is generally considered to be an Eastern Orthodox concept.  Indeed, it is arguably the distinctive underpinning of the Eastern Church's theology and ascetic practice.  But many Western theologians and spiritual writers talk about theosis as well.  One such is Augustine of Hippo.  Alvin Rapien, in a fairly comprehensive article appearing on The Patristic Project site, addresses Augustine's approach to theosis and quotes liberally from his writings.  Three such quotes are reproduced below.

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We carry mortality about with us, we endure infirmity, we look forward to divinity.  For God wishes not only to vivify, but also to deify us.  When would human infirmity ever dared to hope for this, unless divine truth had promised it.
Sermo 23 B

Still, it was not enough for God to promise us divinity in himself, unless he also took on our infirmity, as though to say, "Do you want to know how much I love you, how certain you ought to be that I am going to give you my divine reality?  I took to myself your mortal reality."  We mustn't find it incredible, brothers and sisters, that human beings become gods, that is, that those who were human can become gods.
Sermo 23 B

For the Word, which became flesh, was in the beginning, and was God with God.  But at the same time his participation in our inferior condition, in order to our participation in his higher state, held a kind of medium in his birth of the flesh...So also, just as his inferior circumstances, into which he descended to us, were not in every particular exactly the same with our inferior circumstances in which he found us here.  So our superior state, into which we ascend to him, will not be quite the same as his superior state, in which we find him.  For we by his grace are to be made the sons of God, whereas he was evermore by nature the Son of God.  We, when we are converted, shall cleave to God, though not as his equals.  He never turned from God, and remains ever equal to God; we are partakers of eternal life, he is eternal life.
On Merit and the Forgiveness of Sins, and the Baptism of Infants