According to the stuff.co.nz website, Rahman Ali fears the 71-year-old former heavyweight champion, who has Parkinson's disease, is in terminal decline, British newspaper The Sun reported.
"My brother can't speak - he doesn't recognise me. He's in a bad way. He's very sick," Rahman Ali said.
"It could be months, it could be days. I don't know if he'll last the summer. He's in God's hands. We hope he gently passes away."
Rahman Ali said that before his brother's health went into its latest decline he had said he was not in pain.
"He grabbed my arm and whispered, 'Rah, I've achieved everything I've ever wanted to accomplish. Don't cry for me, I'm in no pain'."
Rahman Ali, who was also a boxer in his youth, also said he had been cut from Muhammad Ali's life.
"We've all been pushed out. The only time I get to see him is at public events," he said
He also revealed Muhammad Ali wanted to be buried in Louisville with a quote from civil rights leader Martin Luther King Jr on his headstone.
"On his tombstone, he said he wanted the Martin Luther King quote, 'I tried to love somebody, I did try to feed the hungry. I did try, in my life, to clothe those who were naked. I want you to say that I tried to love and serve humanity.' The Greatest."