In my top 10 reasons why you need the Septuagint I conclude with the #1 reason being that the Gospel writers record Jesus’ words as occasionally matching the Old Greek of the Hebrew Bible against the Hebrew. This has become a new research interest of mine, and there is no lack of scholarly opinion on the issue! It’s hard to tell if there’s scholarly consensus. The conventional wisdom seems to be that Jesus spoke Aramaic and read from and recited Hebrew scrolls, but that’s certainly not a universal view, from what I can tell. For example, Stanley E. Porter suggests:
… Jesus not only had sufficient linguistic competence to converse with others in Greek but also even to teach in Greek during his ministry.
…I believe that, first, it can be firmly established that Jesus did speak Greek and that we do indeed have some of his actual words.