Some writers/commentators have raised this possibility over the years.
There are most certainly examples of quotations in the New Testament which are taken from outside the Old Testament Scriptures. For example on three occasions Paul quotes heathen poets. Two are very obviously quotations from heathen poets as Paul clearly states this to be the case. The third is maybe not so obvious:
1. Acts 17:28: For in him we live, and move, and have our being; as certain also of your own poets have said, For we are also his offspring.
2. 1 Corinthians 15:33: Be not deceived: evil communications corrupt good manners. The respected John Gill said of this text: This is a sentence [speaking about the words that are underlined] taken out of Menander, an Heathen poet, showing how dangerous is the conversation of evil men, and what an influence bad principles communicated and imbibed, have on the lives and practices of men.
3. Titus 1:12: One of themselves, even a prophet of their own, said, The Cretians are alway liars, evil beasts, slow bellies.
If heathen poets are quoted in the New Testament then there is no barrier to quoting from other sources/writers who are Christian. It is suggested by some writers/commentators that there are a number of such quotations in the New Testament taken from other Christian sources, including hymns, canticles and doxologies, that were known among the early New Testament Church.
These hymns/canticles/doxologies are evidently not taken from the Psalter but are compositions made by others from the Christian era and quoted by some of the New Testament writers. The last thing an exclusive psalmist would want you to do is to quote a hymn in worship!
Some of the suggested New Testament hymns/doxologies include:
1. Philippians 2:6-11: Who, being in the form of God, thought it not robbery to be equal with God: But made himself of no reputation, and took upon him the form of a servant, and was made in the likeness of men: And being found in fashion as a man, he humbled himself, and became obedient unto death, even the death of the cross. Wherefore God also hath highly exalted him, and given him a name which is above every name: That at the name of Jesus every knee should bow, of things in heaven, and things in earth, and things under the earth; And that every tongue should confess that Jesus Christ is Lord, to the glory of God the Father.
2. Colossians 1:15-20: Who is the image of the invisible God, the firstborn of every creature: For by him were all things created, that are in heaven, and that are in earth, visible and invisible, whether they be thrones, or dominions, or principalities, or powers: all things were created by him, and for him: And he is before all things, and by him all things consist. And he is the head of the body, the church: who is the beginning, the firstborn from the dead; that in all things he might have the preeminence. For it pleased the Father that in him should all fulness dwell; And, having made peace through the blood of his cross, by him to reconcile all things unto himself; by him, I say, whether they be things in earth, or things in heaven.
3. 1 Timothy 3:16: And without controversy great is the mystery of godliness: God was manifest in the flesh, justified in the Spirit, seen of angels, preached unto the Gentiles, believed on in the world, received up into glory.
6. Titus 3:4-7: But after that the kindness and love of God our Saviour toward man appeared, Not by works of righteousness which we have done, but according to his mercy he saved us, by the washing of regeneration, and renewing of the Holy Ghost; Which he shed on us abundantly through Jesus Christ our Saviour; That being justified by his grace, we should be made heirs according to the hope of eternal life.
7. Hebrews 1:3,4: Who being the brightness of his glory, and the express image of his person, and upholding all things by the word of his power, when he had by himself purged our sins, sat down on the right hand of the Majesty on high; Being made so much better than the angels, as he hath by inheritance obtained a more excellent name than they.
8. Revelation 1: 5-8: …Unto him that loved us, and washed us from our sins in his own blood, And hath made us kings and priests unto God and his Father; to him be glory and dominion for ever and ever. Amen. Behold, he cometh with clouds; and every eye shall see him, and they also which pierced him: and all kindreds of the earth shall wail because of him. Even so, Amen.
Romans 1:25: Who changed the truth of God into a lie, and worshipped and served the creature more than the Creator, who is blessed for ever. Amen.
Romans 9:5: Whose are the fathers, and of whom as concerning the flesh Christ came, who is over all, God blessed for ever. Amen.
Romans 11:36: For of him, and through him, and to him, are all things: to whom be glory for ever. Amen.
Romans 15:33: Now the God of peace be with you all. Amen.
Romans 16:20: And the God of peace shall bruise Satan under your feet shortly. The grace of our Lord Jesus Christ be with you. Amen.
Romans 16:24: The grace of our Lord Jesus Christ be with you all. Amen.
Romans 16:27: To God only wise, be glory through Jesus Christ for ever. Amen.
Galatians 1:5: To whom be glory for ever and ever. Amen.
Ephesians 3:21: Unto him be glory in the church by Christ Jesus throughout all ages, world without end. Amen.
Philippians 4:20: Now unto God and our Father be glory for ever and ever. Amen.
1 Timothy 1:17: Now unto the King eternal, immortal, invisible, the only wise God, be honour and glory for ever and ever. Amen.
1 Timothy 6:16: Who only hath immortality, dwelling in the light which no man can approach unto; whom no man hath seen, nor can see: to whom be honour and power everlasting. Amen.
2 Timothy 4:18: And the Lord shall deliver me from every evil work, and will preserve me unto his heavenly kingdom: to whom be glory for ever and ever. Amen.
Hebrews 13:21: Make you perfect in every good work to do his will, working in you that which is wellpleasing in his sight, through Jesus Christ; to whom be glory for ever and ever. Amen.
1 Peter 4:11: If any man speak, let him speak as the oracles of God; if any man minister, let him do it as of the ability which God giveth: that God in all things may be glorified through Jesus Christ, to whom be praise and dominion for ever and ever. Amen.
1 Peter 5:11: To him be glory and dominion for ever and ever. Amen.
2 Peter 3:18: But grow in grace, and in the knowledge of our Lord and Saviour Jesus Christ. To him be glory both now and for ever. Amen.
Jude 25: To the only wise God our Saviour, be glory and majesty, dominion and power, both now and ever. Amen.
1. The terms 'Psalms, Hymns and Spiritual Songs' inEphesians 5:19 & Colossians 3:16 do not refer to the 150 Psalms of the Book of Psalms.
2. Old Testament and New Testament saints did not live by this exclusive psalmist rule.
3. The angels and glorified saints did not sing the psalms.