Christians can give serious historical reasons for thinking that some sayings attributed to Jesus go back to him. But those methods do not prove that every biblical wording is verbatim revelation, nor do they override the Quran's correction where the two disagree.
The strongest Christian case
A thoughtful Christian will not usually say, "We know Jesus said this because the Bible says so." The stronger argument is historical. The Gospels are early compared with many ancient sources, they preserve Palestinian Jewish details, some sayings appear in more than one stream of tradition, and certain reports would have been awkward to invent. Christians also point to manuscript evidence showing that the text of the New Testament, though containing variants, is broadly recoverable.
They may add that Jesus' words often have Semitic patterns behind the Greek, which suggests older Aramaic material. They also argue that the earliest Christian communities would not have allowed total fabrication while eyewitnesses or their students were still alive. Taken at its best, this is not a foolish argument. It is a real historical case for continuity between Jesus and parts of the Gospel tradition.
What this can actually prove
Historical method works with probability, not revelation-level certainty. It may justify saying, "This saying is likely early," or "This teaching fits what we know of Jesus' setting." It can support the view that Jesus preached repentance, worship of the one God, the coming judgment, mercy, prayer, and moral purification.
But it cannot prove that every speech in John, Matthew, Mark, or Luke is the exact wording of Jesus. The Gospels are in Greek, while Jesus primarily taught in Aramaic. They were written decades later, arranged with theological aims, and they differ in wording and sequence. Ancient biography allowed paraphrase and arrangement more freely than modern quotation. None of this means the texts are worthless. It means the claim must be modest.
The Quranic correction
Islam does not teach that Jesus was a liar or that his true message disappeared without trace. The Quran honors him as Messiah, prophet, and messenger, and affirms that God gave him revelation:
"And We sent, following in their footsteps, Jesus, the son of Mary, confirming that which came before him in the Torah; and We gave him the Gospel, in which was guidance and light..."
Quran 5:46
At the same time, the Quran presents itself as the final criterion over previous scripture:
"And We have revealed to you the Book in truth, confirming that which preceded it of the Scripture and as a criterion over it."
Quran 5:48
So when the New Testament preserves teachings that agree with pure monotheism, worship, repentance, and righteousness, Muslims can recognize their closeness to Jesus' mission. When it attributes divine sonship, incarnation, or worship of Jesus to the message of Jesus, the Muslim answer is that this conflicts with the final revelation and with the prophetic pattern.
"O People of the Scripture, do not commit excess in your religion or say about Allah except the truth. The Messiah, Jesus, the son of Mary, was only a messenger of Allah..."
Quran 4:171
A fair Muslim position
The Prophet (PBUH) taught caution regarding reports from earlier scriptures:
"Do not believe the People of the Scripture, and do not disbelieve them, but say: We believe in Allah and what has been revealed to us."
Sahih al-Bukhari
This is balanced. We do not mock the Bible or pretend there is no history in it. Nor do we grant it the same preservation and authority as the Quran. Christian historical arguments can establish that some Gospel material is early and plausible. They do not establish that the present Bible gives us every statement of Jesus with certainty, or that later theological claims are binding over the Quran.
The honest result is this: history may recover echoes of Jesus' voice, but revelation is needed to judge them with certainty. For Muslims, that criterion is the Quran.