William, 27, last visited Australia as a nine-month-old baby in 1983 with his parents Prince Charles and the late Princess Diana, who was killed in a car crash in Paris in 1997.
"He has his mother's heart. And I think a lot of people will respect him because of this mother," said Mundine.
From his first-floor office window overlooking The Block, Mundine can see a group of men, some clearly under the influence. One throws a bottle at two young children in his way.
Mundine said some radicals within the indigenous community might question why he would want to shake William's hand given the injustices his people have suffered since a British penal colony was established in Australia in 1788.
"But that's the past," he said. "We're paving the way for the new generation."
"I'll just show him all the respect I can. He's the prince now but he could be the king. He's coming to The Block. We are not going to hide nothing."
Indigenous social justice campaigner Tom Calma said it was important that visiting dignitaries such as William, who will also tour bushfire-ravaged areas outside of Melbourne, were allowed to see the real Australia.
"It's not good enough that they get a sanitised version of our history or a sanitised version of our lifestyle here," said Calma, the country's Aboriginal and Torres Strait Islander Social Justice Commissioner.
"It's the old 'warts and all.' We need to be able to show it as it is."
William, who will be in Australia from January 19 to 21, will also be asked to help return the remains of Aborigines, including skulls and bones, often taken as curiosities and which now lie in foreign museums.
"We're saying it's time to help us heal and return our remains," Rob Welsh, of the Redfern-based Metropolitan Aboriginal Land Council, told AFP.
Of particular importance is the head of the great Aboriginal warrior Pemulwuy who fought against the British occupation and was ultimately shot dead on the governor's orders in 1802. His head is believed to have been sent by ship to England shortly afterwards but its location is unknown.
Welsh, among those who will meet the prince on Tuesday, said he was overwhelmed by the prospect of meeting a royal, despite the past conflicts between indigenous Australians and their former colonial rulers.
"He's definitely one of the stand-out royals, him and Harry. And I was very impressed for him to offer to come to Redfern," he said.
Welsh said while some differences would remain, "we've got to move forward."
"We can't judge William on what his grandparents have done and so on. And he seems like the prince that is ready to come out and listen to the community, listen to the people," he said.
"He's already lined up for Disneyland with his mother as a child. He's gone down and slept out at night on freezing cold nights."
Asked whether William would be bringing his mother's legacy to Redfern, Welsh said the young royal "does fill that gap for us."
Lani Tuitavake, who has lived and worked in The Block for 18 years, said the visit was a chance to showcase the improvements that have come to the neighbourhood through the hard work of the past decade.
Some of the worst terraces have been demolished, efforts have been made to stop the sale of drugs and there are plans, known as the Pemulwuy Project, to redevelop the area to build quality housing for indigenous families.
"To the community and to me it highlights the change," she said. "Scotland Yard... they are not going to put their precious prince and future king in harm's way."