Fielder-Civil, 30, has battled addictions to drugs and alcohol for years and spent time in prison for assault.
The Sun said he is on life support at a hospital in Dewsbury, West Yorks, after he was found choking in bed during a night of binge drinking and consuming drugs.
Fielder-Civil, the father of a 15-month-old boy, had suffered multiple organ failure as a result of the incident, which took place late last month, a few days after the first anniversary of his ex-wife's death.
Winehouse died last year of accidental alcohol poisoning at the age of 27. She was married to Fielder-Civil from 2007-09.
"The doctors say they don't know the prognosis. They said they put him in a coma to help him and due to infection," Sarah Aspin, his son's mother, told the newspaper. "I'm praying he'll survive, but I'm having to prepare myself that he may never wake up."
"Remember Amy loved him. Let's pray for his recovery," Fielder-Civil's former father-in-law, Mitch Winehouse, said via Twitter.