"The news about Joe is hard to believe and even harder to accept," Ali said in a statement. "Joe is a fighter and a champion, and I am praying he is fighting now."
Frazier was diagnosed with liver cancer about a month ago, and his manager, Leslie Wolff, said "nothing major" had changed in his health on Sunday.
The legendary heavyweights squared off three times in the 1970s, with Ali winning the last two bouts. Their first meeting was billed "The Fight of the Century" and their third "The Thrilla in Manila."
In 1996, after Ali lit the Olympic torch in Atlanta, Frazier told Inquirer columnist Bill Lyon that "if it had been me [there], he'd have been pushed into the fire."
At a news conference later that year, Frazier said he hoped to mend his relationship with Ali.
"We got to do it, before we all close our eyes, because I want to see him in heaven," Frazier said.
While promoting their fights, Ali infamously labeled Frazier an "Uncle Tom" and a "gorilla."
It was Frazier who petitioned President Richard Nixon to intervene to have Ali's boxing license reinstated after Ali refused induction into the U.S. Army during the Vietnam War. Frazier also boycotted the tournament to crown a new champion after Ali was stripped of the title in 1967.
Both Wolff and Ali's publicist, Craig Bankey, said they believed the two to be on good terms, as they had done a photo shoot together at Frazier's now-shuttered North Philadelphia gym a few years ago.
On Sunday, Frazier remained under heavy medication and slept most of the day, according to Wolff.
"But, when he does wake up, he carries on a conversation with his companion," Wolff said.
"My family and I are keeping Joe and his family in our daily prayers," Ali said in his statement. "Joe has a lot of friends pulling for him, and I'm one of them."
Along with the message from Ali, Frazier received calls from the boxing communities in England and Ireland and fellow heavyweight champions Larry Holmes and Leon Spinks, according to Wolff.
Contact staff writer Matt Breen at firstname.lastname@example.org or @matt_breen on Twitter.