"He needs every bit of fight he's got left to survive," a source told the site.
"Doctors are telling the family that it likely won't be long until he passes away."
Diagnosed with Parkinson's over 30 years ago, Ali has looked increasingly frail in public appearances, including in April when was seen hunched over and wearing sunglasses 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 him, held at the Muhammad Ali Center in his hometown of Louisville, Kentucky.
His doctor, Abraham Lieberman, said he could not discuss his condition.
"I can't really say much more than what's in the papers," he said.
An iconic figure who at one point was perhaps the most recognised person in the world, Ali has nine children by four different wives and two other relationships. The sporting superstar has lived quietly in the Phoenix area with his fourth wife, Lonnie, whom he married in 1986.
