De Minaur will take on rising American Alex Michelsen in the fourth round on Monday night also trying to match Lleyton Hewitt's effort in reaching the last eight at four successive grand slams some 20 years ago.
Rafter is backing the world No.8 to see off the Michelsen threat while also relishing the opportunity to help take de Minaur's game to even greater heights in his new role as vice-captain of Team World for this year's Laver Cup.
The former world No.1 and dual US Open champion is joining forces with Andre Agassi as Team World squares off with Team Europe in San Francisco is September.
De Minaur will be one of Rafter's spearheads.
Rafter says he's looking forward to working with the 'exciting' de Minaur at the Laver Cup. (Jono Searle/AAP PHOTOS)
"I think there's some things I can help him with," Rafter said at Melbourne Park.
"I can help him wiith transition to the net, but he's very good. He's getting better and better all the time.
"So it's exciting and if I can help Alex in any way - I might only get that one week - but it might flow on somewhere else.
"He's a kid who really wants to learn, really wants to develop his game."
Should de Minaur beat Michelsen, the world No.42 who has already eliminated two top-20 rivals from the Australian Open draw, he will face either top-ranked defending champion Jannik Sinner or 14th seed Holger Rune on Wednesday for a spot in the semi-finals.
In Monday's other two fourth-round affairs, veteran Frenchman Gael Monfils faces US 21st seed Ben Shelton and American teenage qualifier Learner Tien plays unseeded Italian Lorenzo Sonego.
German qualifying lucky loser Eva Lys takes centre stage in the women's event against second-seeded five-time grand slam champion Iga Swiatek.
Lys is already the first lucky loser to make the last 16 since the Open moved to Melbourne Park in 1988 and now has the chance to create more tennis history.
The winner will play either American eighth seed Emma Navarro or Russian world No.9 Daria Kasatkina in the quarter-finals.
In the remaining two women's fourth-round battles, 2023 Open runner-up Elena Rybakina takes on American Maddison Keys and Monfils' wife Elina Svitolina continues her own dream run against unseeded Russian Veronika Kudermetova.
24°C