It quoted Franklin herself as saying she had "highly successful" surgery last week.
"God is still in control. I had superb doctors and nurses whom were blessed by all the prayers of the city and the country," she said.
The Detroit News meanwhile reported she had pancreatic cancer, which has the highest mortality rate of all major cancers, killing around 95 percent of patients within five years of diagnosis.
Representatives for Franklin, who rose from singing gospel in Detroit to top charts in the 1960s and 1970s with hits like "Respect," "Think" and "Chain of Fools," did not immediately respond to requests for confirmation.
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