Citing an unnamed source, the newspaper said Frazier, 67, was in hospice care "in serious shape" and has only a short time to live.
Frazier was at his peak in the late 1960s and early 1970s, when he fought Muhammad Ali in three memorable heavyweight bouts, one of which he won -- held March 8, 1971, in Madison Square Garden.
The best-remembered of the three was the 1975 "Thrilla in Manila." In that fight in the Philippines, Frazier's trainer, Eddie Futch, stopped the event after the 14th round with Ali ahead on points.
Frazier lost to George Foreman in a five-round technical knockout in his following fight, held the next June.
Frazier, a member of boxing's Hall of Fame, finished with a 32-4-1 professional record with 27 knockouts.
Frazier also took home the gold medal from the 1964 Olympics in Tokyo.
Celebrity Families of 2014 [PHOTOS]