That's also the belief of the Catholic Church.
CCC 460 The Word became flesh to make us "partakers of the divine nature": "For this is why the Word became man, and the Son of God became the Son of man: so that man, by entering into communion with the Word and thus receiving divine sonship, might become a son of God." "For the Son of God became man so that we might become God." "The only-begotten Son of God, wanting to make us sharers in his divinity, assumed our nature, so that he, made man, might make men gods."
(John 10:32-36)
Jesus tells the Pharisees, who want to stone Him, that since God in the Old Testament said to the men to whom the word of God came "I have said you (plural) are gods (plural)" (Psalm 82:6), how can they stone him for claiming to be God's son?
God calls men gods in a certain sense in Psalm 82, and Jesus uses this to defend his divinity. So here's nothing wrong with the word "gods." It's the Biblical word that God spoke, Himself.
It's all tied in with the Incarnation of Christ. The Incarnation is the wonderful union of the divine and human natures in the one Person of the Word.
(2 Peter 1:4):
"Through these, he has bestowed on us the precious and very great promises, so that through them you may come to share in the divine nature, after escaping from the corruption that is in the world because of evil desire."
God does not say that we become part of the Trinity.
God does not say that we become divine Persons like the Father and the Holy Spirit.
God does not say that we become 'gods' in the pagan/polytheistic sense.
But indeed God does He calls us 'gods' in the sense of being partakers in His divine nature. It is only by being united to Christ that we share in His divine nature. (John 6:51-69) We are not participants (partakers, sharers) in the divine nature apart from Christ.
The Eastern Churches, teaching the exact same doctrine but using different terminology, speak of participating in the 'energies' of God, as opposed to his 'essence'. We don't become one in being (consubstantial) (one in esence) with the Father, Son and Holy Spirit; we don't join the Holy Trinity. Rather we participate in their 'energies'. We become saved by being transformed into his likeness from glory to glory (2 Corinthians 3:18). In other words, we become more and more like Him, until finally we see Him face to face:
(1 John 3:2)
"Dear friends, now we are children of God, and what we will be has not yet been made known. But we know that when he appears, we shall be like him, for we shall see him as he is."
"I have said you (plural) are gods (plural)" (Psalm 82:6).
This is the doctrine of the Church because this is the doctrine of the Bible.