A sentence is provided in direct speech. He said, “I am not feeling well.”

Explanation

In indirect speech, when the reporting verb is in the past tense (said), the tense of the reported speech usually shifts back:
am → was
Also, the pronoun I changes to he.
So,
Direct: He said, "I am not feeling well."
Indirect: He said that he was not feeling well.

He said that he is not feeling well. – Incorrect (no backshift of tense)
He said that he was not feeling well. – Correct
He said that he didn't felt well. – Incorrect ("didn't" should be followed by the base form feel)
He said he not feeling well. – Incorrect sentence structure
Correct Answer: He said that he was not feeling well.