Reports on Friday night circulated that Calzaghe, the father and trainer of world champion Joe Calzaghe, had died aged 69.
But those have been confirmed as incorrect and the Italian-born coach is still alive.
The father of fighter Joe is however suffering with illness and Carrie has asked for privacy for the family at this difficult time.
Enzo’s niece Carrie said on Facebook: “Enzo Calzaghe, my uncle, has not passed away. This is false news.
“He is alive but very poorly. Please allow space for our family at this time.
“He is alive and still fighting. We will keep you posted and let you know how he is doing when we can. Please allow and respect our privacy at this time.
“Thank you, team Calzaghe. Please share.”
Tributes poured in from across the boxing world via social media in response to the initial reports.
Enzo oversaw son Joe’s WBO, WBC and WBA super-middleweight title triumphs.
The pair spent 18 years together unbeaten in the amateur and professional ranks across 46 fights until Joe’s retirement in February 2009.
Joe’s glittering career was rewarded with a place in the Hall of Fame having secured major wins over the likes of Jeff Lacy, Mikkel Kessler, Chris Eubank, Roy Jones Jr. and Bernard Hopkins with his dad crucial to all of his successes.
Southpaw Joe is the only ever undefeated British world champion.