No…no NT writing ever intimated Jesus intending to have them write something.
From Luke 10: 16 “Whoever listens to you listens to me; whoever rejects you rejects me; but whoever rejects me rejects him who sent me.”
He did not say…he who reads.
catholicapologetics.info/apologetics/protestantism/wbible.htm
From Chapter 3:
Our Blessed Lord Himself never, so far as we know, wrote a line of Scripture—certainly none that has been preserved. He never told His Apostles to write anything. He did not command them to commit to writing what He had delivered to them: but He said, ‘Go ye and teach all nations’, ‘preach the Gospel to every creature’ , ‘He that heareth you heareth Me’. What He commanded and meant them to do was precisely what He had done Himself, viz.—deliver the Word of God to the people by the living voice—convince , persuade, instruct, convert them by addressing themselves face to face to living men and women; not intrust their message to a dead book which might perish and be destroyed, and be misunderstood and misinterpreted and corrupted, but adopt the more safe and natural way of presenting the truth to them by word of mouth, and of training others to do the same after they themselves were gone, and so by a living tradition, preserving and handing down the Word of God as they had received it, to all generations.