Mat_22:29 But Jesus answered them, "You are wrong, because you know neither the Scriptures nor the power of God.
Mat_26:54 But how then should the Scriptures be fulfilled, that it must be so?"
Luk_24:44 Then he said to them, "These are my words that I spoke to you while I was still with you, that everything written about me in the Law of Moses and the Prophets and the Psalms must be fulfilled."
There wasn't any question about what our Lord Jesus was talking about. The OT was already codified.
The Septuagint may have been used along with a lot of other writings, but what was the tradition of the time?