The 74-year-old boxing great's respiratory issues have been complicated by the Parkinson's that he was diagnosed with in the 1980s, two people told The Associated Press a day earlier.
The two spoke separately in describing Ali's condition as being very concerning to family members. They declined to be identified because they were not speaking on behalf of the family.
Several of Ali's daughters reportedly flew to Phoenix late Thursday and early Friday to be with their father.
PHOTOS: MUHAMMAD ALI THROUGH THE YEARS
Laila Ali, herself a former boxing champion, posted a picture Friday afternoon on Facebook of her father holding her daughter when she was an infant.
"I love this photo of my father and my daughter Sydney when she was a baby!" she wrote. "Thanks for all the love and well wishes. I feel your love and appreciate it!!"
A spokesman for the former heavyweight champion said in an email Friday that there was no update on his condition. Spokesman Bob Gunnell said a day earlier that Ali was in fair condition and that a brief hospital stay was expected.
Ali's longtime Parkinson's doctor declined comment when reached by the AP Thursday night.
"I can't really say much more than what's in the papers," said Dr. Abraham Lieberman of the Barrow Neurological Institute in Phoenix.
Ali has been hospitalized several times in recent years, most recently in early 2015 when he was treated for a severe urinary tract infection initially diagnosed as pneumonia.
Ali has looked increasingly frail in public appearances, including April 9 when he wore sunglasses and was hunched over at the annual Celebrity Fight Night dinner in Phoenix, which raises funds for treatment of Parkinson's.
His last formal public appearance before that was in October when he appeared at the Sports Illustrated Tribute to Muhammad Ali at The Muhammad Ali Center in his hometown of Louisville, Kentucky, along with former opponents George Foreman and Larry Holmes.
Ali has suffered from Parkinson's for three decades, most famously trembling badly while lighting the Olympic torch in 1996 in Atlanta. Despite the disease he kept up a busy appearance schedule until recently, though he has not spoken in public for years.
Doctors say the Parkinson's likely was caused by the thousands of punches Ali took during a career in which he traveled the world for big fights.
An iconic figure who at one point was perhaps the most recognized person in the world, Ali has lived quietly in the Phoenix area with his fourth wife, Lonnie, whom he married in 1986.
News of his hospitalization brought well wishes from boxers and others on Twitter, including Sugar Ray Leonard, who modeled his career after Ali's.
"Prayers & blessings to my idol, my friend, & without question, the Greatest of All Time MuhammadAli ! #GOAT," Leonard wrote.