"I know the doctors who are working with him are very good people, very good doctors and are doing an excellent job. I am quite certain that one of these days Madiba will go back home," national broadcaster SABC reported Mbeki as saying.
"What the government has been saying, that his condition is critical but stable, is correct, that one of these days the doctors will agree that he can go and stay at home rather than in hospital."
Mandela, also known by his clan name Madiba, turns 95 next week. He has been in hospital since June 8 for a recurring lung infection that has led to four hospital stays in the past six months.
Mandela's wife Graca Machel told local eNCA news he was showing signs of improvement.
"He continues to respond positively to treatment. I would say that today I am less anxious than I was a week ago," she said.
Mandela was elected president of a multiracial South Africa in 1994, four years after being released from prison.