Throughout the centuries, the Muslim world has argued that the Qur'an is to be read as sola scriptura, with supplementation only from fairly late hadith accounts, but never from the Bible. This is determined through the latehadith literature where the literary character of Muhammad is claimed to have forbidden Umar from reading the Bible.
In contrast to this, Shi`ah accounts, from Muhammad's direct descendants through `Ali and Fatimah, claim that these descendants - spiritual a'immah - were extremely well versed in the Bible. Similarly, such accounts contend that the Bible would be a primary source of judgment for a future "mahdi", who would also pray in the Hebrew language. While such accounts are repleat throughout the Shi`ah hadith literature - itself being writting as late as the Sunni accounts - normative Ithna `Ashari beliefs today are much closer to mainstream Sunni views, and than they are to the actual hadithnarrations attributed to the Ahl al-Bayt, Muhammad's family, with regard to such matters.
As for the Qur'an itself, it is even more clear; mincing no words whatsoever, and having no awareness of any later notion that it should supercede, or abrogate the Bible. We read, for instance, that if something is already in the Bible, the follower of Muhammad has no business asking him for a decision on such a matter; which is already plainly commanded by God in the Bible.
وَكَيْفَ يُحَكِّمُونَكَ وَعِنْدَهُمُ التَّوْرَاةُ فِيهَا حُكْمُ اللَّهِ ثُمَّ يَتَوَلَّوْنَ مِنْ بَعْدِ ذَٰلِكَ ۚ وَمَا أُولَٰئِكَ بِالْمُؤْمِنِينَ
And why do they come to you for a decision, when they have the Torah before them? Therein is the Command of God; yet even after that, they would turn away. Such are not Believers (Mu'minin/Ma'minim). (5.43)
فَإِنْ كُنْتَ فِي شَكٍّ مِمَّا أَنْزَلْنَا إِلَيْكَ فَاسْأَلِ الَّذِينَ يَقْرَءُونَ الْكِتَابَ مِنْ قَبْلِكَ ۚ لَقَدْ جَاءَكَ الْحَقُّ مِنْ رَبِّكَ فَلَا تَكُونَنَّ مِنَ الْمُمْتَرِينَ
If you are in doubt as what We have revealed to you, ask those who have been reading the Bible before you. Verily, the truth from your Lord has come to you, so be not of those who waiver [in belief]. (10.94)
Criticizing those who don't adhere to the Torah and Gospel, only hypocrites are criticized, and not Jews and Nazarenes across the board. This tells us that the Qur'an viewed the Torah and the singular Gospel used by the Nazarenes, according to historical sources, a singular Hebrew Gospel which the Ebionites and Nazarenes alike utilized, as being valid, and does not criticize it as being textually invalid or corrupted.
وَلَوْ أَنَّهُمْ أَقَامُوا التَّوْرَاةَ وَالْإِنْجِيلَ وَمَا أُنْزِلَ إِلَيْهِمْ مِنْ رَبِّهِمْ لَأَكَلُوا مِنْ فَوْقِهِمْ وَمِنْ تَحْتِ أَرْجُلِهِمْ ۚ مِنْهُمْ أُمَّةٌ مُقْتَصِدَةٌ ۖ وَكَثِيرٌ مِنْهُمْ سَاءَ مَا يَعْمَلُونَ
If only they had stood fast by the Torah, the Gospel, and all the revelation that was sent to them from their Lord, they would have enjoyed happiness from every side. There is from among them a party on the right course: but many of them follow a course that is evil. (5.66)
This clearly says that if those who turned away from the Torah and the Hebrew Ebionite Gospel would have kept to those texts, then they would have enjoyed happiness. This thus precludes the possibility that those scriptures were viewed as corrupt or abrogated by the Qur'an. Furthermore, the Qur'an commands Jews to continue to follow the Brit of the Torah and Mitzvot:
يَا بَنِي إِسْرَائِيلَ اذْكُرُوا نِعْمَتِيَ الَّتِي أَنْعَمْتُ عَلَيْكُمْ وَأَوْفُوا بِعَهْدِي أُوفِ بِعَهْدِكُمْ وَإِيَّايَ فَارْهَبُونِ
O Children of Israel! call to mind My Favor which I bestowed upon you, and keep up your Covenant with Me as I fulfill My Covenant with you, and fear no one but Me. (2.40)
That is, the Qur'an instructs Jews to continue to practice Yahadut, the praising of Yah through the Covanent of the Mitzvot in the Torah. This is the clearly articulated Covenant to which the Qur'an refers, and which any reader of the Bible is familiar.
The Qur'an in fact says that when those who follow the Bible already hear what Muhammad recited, they recognized it as Biblical and Midrashic stories and instructions ALREADY received.
مُ الْكِتَابَ مِنْ قَبْلِهِ هُمْ بِهِ يُؤْمِنُونَ
Those unto whom We gave the Bible before it, they believe in it (28.52)
وَإِذَا يُتْلَىٰ عَلَيْهِمْ قَالُوا آمَنَّا بِهِ إِنَّهُ الْحَقُّ مِنْ رَبِّنَا إِنَّا كُنَّا مِنْ قَبْلِهِ مُسْلِمِينَ
And when it is recited to them they say: We believe in it surely it is the truth from our Lord; surely we were submitting ones (muslimin) before this. (28.53)
Clearly then, a "muslim" is here defined as one who believes in the Bible and follows it. This was a new message to polythesists in the Arab world, but it was nothing at all new to Jews and Nazarenes. Thus, the Qur'an says, to its polytheist audience, that the Jews and Nazarenes in their midst already know this and are the first to say "we were submitting ones before this"; indicating clearly that "muslim" was not a term for a separate religion, defined by the Qur'an (but instead was a universal practice of obeying God by honoring the instructions in the Bible or the instructions given by Muhammad to the Arabs who had not previously been exposed to the Bible and Midrash. Thus the Qur'an tells us to "And believe in what I have revealed, verifying that which is with you, and be not the first to deny it, neither sell My communications for a small price; and Me, Me alone should you fear" (2.41).
وَآمِنُوا بِمَا أَنْزَلْتُ مُصَدِّقًا لِمَا مَعَكُمْ وَلَا تَكُونُوا أَوَّلَ كَافِرٍ بِهِ ۖ وَلَا تَشْتَرُوا بِآيَاتِي ثَمَنًا قَلِيلًا وَإِيَّايَ فَاتَّقُونِ
Thus, the Bible which the Qur'an is "verifying" is "with you" currently, in Muhammad's day and ever since. 'Ayah 89 also repeats that the Qur'an is "verifying" the Bible, and that the curse of Allah is on the "kafirin", the "koferim" in Hebrew; meaning those who apostate from Judaism by breaking the Covanent. The Bible is not seen as corrupted, nor filled with deformed and distorted accounts that the listener to the Qur'an is to disregard. When Muslims reject the Bible, they are literally rejecting and disobeying the Qur'an.