Several news sources have reported the anti-apartheid icon has been released from hospital to return to his home in Johannesburg.
CNN says two sources close to Mandela had confirmed his release, while Sky says his daughter has confirmed the report.
But South African president Jacob Zuma says the reports are incorrect.
"Madiba is still in hospital in Pretoria, and remains in a critical but stable condition. At times his condition becomes unstable, but he responds to medical interventions," the presidency said in a statement on its website.
Nelson Mandela was admitted with a recurring lung infection on 8 June.
His condition was last week described as "critical but stable", and there has been no official update on his health since then.
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