Leo Mugabe however declined to discuss the $10-million retirement bonus reportedly granted to the 93-year-old former president as part of a deal that finally persuaded him to resign on Tuesday.
"He is fine. I have been to see him, he is quite jovial," the son of Mugabe's late sister Sabina told AFP.
"He is actually looking forward to his new life -- farming and staying at the rural home. He has taken it well."
But he added that Mugabe's wife Grace was now concentrating on plans to build a university in his honour.
"I like the spirit she has, she is with him all the time. She is an amazing person. She wants to continue planning the Robert Mugabe University so they have something to do," he said.
Zimbabwe announced plans in August to build the $1-billion post-graduate university in Mazowe, 35 kilometres (20 miles) outside Harare.
The plan drew fierce criticism as Mugabe is accused of brutal repression and bringing the country to economic ruin.
In the exit negotiations, Mugabe was granted a $10-million lump sum, full immunity and allowed to keep his assets, according to the respected Zimbabwe Independent newspaper.
He will still be paid his full salary, in line with constitution, while Grace Mugabe will reportedly receive half his pay after his death.
Asked about the deal, Mugabe's long-time spokesman George Charamba told AFP that "the package of a retiring president will be defined (by) law".
He earlier said immunity had never been discussed during the talks between the president and the army chiefs who briefly put Mugabe under house arrest.
Mnangagwa, a former close ally of Mugabe for decades, has vowed sweeping changes to revive the country's moribund economy.
In his inaugural address on Friday, Mnangagwa also paid tribute to Mugabe, describing him as one of the "founding fathers of our nation".
Critics fear Mnangagwa -- who has been accused of overseeing violence and ethnic massacres -- could prove as authoritarian as his predecessor.
Calls for justice
Mugabe had ruled Zimbabwe since independence in 1980, exercising almost total authority to crush any sign of dissent during a reign characterised by brutality, rigged elections and international isolation.
Until his rule ended Tuesday with a resignation letter sent to MPs who had gathered to impeach him, he was the world's oldest head of state.
Activist pastor Evan Mawaire called on Sunday for Mugabe to face justice, saying that further demonstrations could erupt if people believe there was no accountability for decades of state crimes.
"A lot of people in this country have been wronged and oppressed, it is important they see justice playing out," Mawaire told AFP after preaching at his small church in Harare.
"(If) he is not prosecuted that takes away a sense of closure. It is important for these criminals to be followed up to show the nation that the law catches up with them."
Mugabe made a defiant televised address last Sunday two days before he resigned, but he and his wife's current whereabouts is not known.
On Friday, a high court ruled that the military takeover was legal, raising concerns about the army's future influence and the rule of law under the new administration.