A sheikh asks and says: We see some imams do not recite the basmala aloud.

Yes, regarding reciting the basmala aloud, we say there is no authentic hadith from the Prophet ﷺ about reciting the basmala aloud in prayer.

The best narration on this is the hadith of Nu'aym from Abu Huraira, may Allah be pleased with him.

He said: I lead you in prayer as the Messenger of Allah ﷺ prayed, so he recited "In the name of Allah, the Most Merciful, the Most Compassionate. All praise is due to Allah, Lord of the worlds."

Some imams, like the Shafi'is, followed this hadith, but the majority of scholars hold that the basmala is not recited aloud, and there is no authentic hadith about reciting it aloud.

From the Prophet ﷺ. As for reciting it silently, that is another issue.

That is another issue. The matter is that reciting it is among the recommended acts from the sunnah, and there is no disagreement about that.

Rather, scholars differ regarding reciting it in al-Fatiha. Some consider it a verse of al-Fatiha, and if someone leaves it out, his prayer is invalid. This is a topic discussed by scholars elsewhere.

As for reciting the basmala aloud in al-Fatiha, or also in the surahs if a person wants to recite surahs, we say that nothing is established regarding that, and a person should not recite the basmala aloud, but rather recite it quietly.

And this is correct, and it is also the practice of the majority of the sahaba of the Prophet ﷺ. And Allah knows best.