Short answer
The Quran names 25 prophets, and Isaiah, Jeremiah, Daniel and Samuel are not named among them. Allah says He also sent messengers whose stories He did not tell, so Muslims do not deny them. Many classical historians and commentators counted them as prophets of the Children of Israel, but this rests on reports, not on the Quran or sahih hadith.
Sunni creed requires belief in every prophet the Quran names and in all of Allah's messengers in general. For a figure not named in the Quran or sahih hadith, a Muslim may say he was among the righteous of the Children of Israel and possibly a prophet, without stating it as certain. Al-Nasafi's creed advises not to restrict the prophets to a fixed list or number.
The four schools agree on this.
Explanation
The Quran tells us plainly that the named prophets are not all of them: "messengers about whom We have related [their stories] to you before and messengers about whom We have not related to you" (4:164, also 40:78). So when someone asks about a Biblical figure who is not named in the Quran, the answer is not "he was false" but "Allah knows best".
Some of these figures are close to the Quran's text. Surah al-Baqarah tells of "a prophet of theirs" after Musa whom the Children of Israel asked for a king, and who appointed Talut (Saul) (2:246-247). Many commentators said this prophet was Shamwil (Samuel). Al-Yasa (Elisha) and Ilyas (Elijah) are named in the Quran as prophets. 'Uzayr (Ezra) is named once, in a verse criticising a claim made about him (9:30), and the scholars differed over whether he was a prophet.
Isaiah (Sha'ya), Jeremiah (Irmiya) and Daniel (Danyal) appear in the books of history and tafsir, for example in accounts of the destruction of Jerusalem. Most of that material comes from Israelite reports. The Prophet ﷺ taught a simple rule for such reports: do not confirm them and do not deny them, and say that you believe in what Allah revealed.
So the balanced position is to speak of them with respect, to accept that many scholars counted them as prophets, and to avoid stating it as a fact of faith. What Muslims do not accept are stories, from any source, that attribute serious sins or false teachings to men honoured as prophets. See the list of the 25 prophets named in the Quran and how many prophets there are.
The evidence
Quran, Surah An-Nisaa 4:164
وَرُسُلًۭا قَدْ قَصَصْنَٰهُمْ عَلَيْكَ مِن قَبْلُ وَرُسُلًۭا لَّمْ نَقْصُصْهُمْ عَلَيْكَ ۚ وَكَلَّمَ ٱللَّهُ مُوسَىٰ تَكْلِيمًۭا ﴿١٦٤﴾
And [We sent] messengers about whom We have related [their stories] to you before and messengers about whom We have not related to you. And Allah spoke to Moses with [direct] speech.
Shows there are prophets whom the Quran does not name.
Quran, Surah Al-Baqara 2:246
أَلَمْ تَرَ إِلَى ٱلْمَلَإِ مِنۢ بَنِىٓ إِسْرَٰٓءِيلَ مِنۢ بَعْدِ مُوسَىٰٓ إِذْ قَالُوا۟ لِنَبِىٍّۢ لَّهُمُ ٱبْعَثْ لَنَا مَلِكًۭا نُّقَٰتِلْ فِى سَبِيلِ ٱللَّهِ ۖ قَالَ هَلْ عَسَيْتُمْ إِن كُتِبَ عَلَيْكُمُ ٱلْقِتَالُ أَلَّا تُقَٰتِلُوا۟ ۖ قَالُوا۟ وَمَا لَنَآ أَلَّا نُقَٰتِلَ فِى سَبِيلِ ٱللَّهِ وَقَدْ أُخْرِجْنَا مِن دِيَٰرِنَا وَأَبْنَآئِنَا ۖ فَلَمَّا كُتِبَ عَلَيْهِمُ ٱلْقِتَالُ تَوَلَّوْا۟ إِلَّا قَلِيلًۭا مِّنْهُمْ ۗ وَٱللَّهُ عَلِيمٌۢ بِٱلظَّٰلِمِينَ ﴿٢٤٦﴾
Have you not considered the assembly of the Children of Israel after [the time of] Moses when they said to a prophet of theirs, "Send to us a king, and we will fight in the way of Allah "? He said, "Would you perhaps refrain from fighting if fighting was prescribed for you?" They said, "And why should we not fight in the cause of Allah when we have been driven out from our homes and from our children?" But when fighting was prescribed for them, they turned away, except for a few of them. And Allah is Knowing of the wrongdoers.
Mentions an unnamed prophet of the Children of Israel whom many commentators identified as Samuel.
Sahih al-Bukhari 4485
Sahih... لاَ تُصَدِّقُوا أَهْلَ الْكِتَابِ وَلاَ تُكَذِّبُوهُمْ، وَقُولُوا آمَنَّا بِاللَّهِ وَمَا أُنْزِلَ ...
"Do not believe the People of the Book and do not call them liars. Say: We believe in Allah and in what has been sent down."
Gives the rule for reports from earlier scriptures that our sources neither confirm nor deny.
Where the ruling is recorded
- al-Aqa'id al-Nasafiyya with Sharh al-Taftazani, Section on the prophets. States that it is better not to restrict the prophets to a set number, so no prophet is left out and no one else added.
- Tafsir Ibn Kathir, Commentary on Surah al-Baqarah, the story of Talut. Reports that the prophet in 2:246 is said to be Shamwil (Samuel).
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.