Tapia died Sunday, a source close to the family said.
Albuquerque police spokesman Robert Gibbs said police were called to Tapia's house about 7:45 p.m. by a family member who found a body there.
Tapia had struggled with drug and alcohol abuse, the Journal said.
Gibbs said the death did not appear suspicious.
The Office of the Medical Investigator will determine the official cause of death after an autopsy.
"To me, he was the most giving person that I know," said Hector Munoz, an Albuquerque professional boxer being trained by Tapia. "I'm just blessed that he did work my corner and that he trained me. He was a great guy, just unbelievable as a trainer, too."
The Journal said between 1990-1993, Tapia was in and out of jail as he battled cocaine and alcohol.
He won the first of five world titles in 1994, defeating Henry Martinez for the WBO junior bantamweight title.
A judge ordered Tapia to attend a drug rehabilitation program in 1995 after an alleged domestic assault incident.
In 2003, Tapia was in a coma for three days and spent several months in a California rehab center.
He was hospitalized in 2007 for an apparent cocaine overdose.
Tapia announced his retirement last year after beating Mauricio Pastrana by decision.