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.