The 52-year-old singer fell ill in April after a blood vessel ruptured in his brain and he was hit by meningitis and pneumonia, the report said.
Friends and family of the star told People magazine that he is in rehabilitation, having five hours of therapy a day on most days.
"His voice is the same as it ever was. He's back," his friend and singer Patti LaBelle said.
Vandross is now learning how to get in and out of a car and does physical exercises to regain his strength, People magazine said.
The singer has sold more than 20 million records during his career, and won four Grammy awards in the 1990s.
His latest album, "Dance With My Father," was released after he fell ill and went to the top on U.S. chart.
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