The mercurial Russian will be de Minaur's next opponent -- and a familiar one -- should the Australian No.1 defeat 26th seed Jakub Mensik later on Friday.
The pair have shared four victories apiece in their eight clashes stretching back to 2018, and Rublev handed de Minaur one of his most painful losses when he ousted the Sydneysider in five sets, also in the last-16, at the Australian Open two years ago.
Between them, the pair have reached 17 quarter-finals in grand slams -- 10 for Rublev, and seven for de Minaur -- but have never managed to progress further.
"Alex have today tough match. Let's see how it's going to be, but Alex, it's obvious that his level is to be in the semi-finals and to compete for the slams.
"He prove it, and he beat players who won slams, who won finals and things like that. So his level is there. It's just, okay, happen, he's been knocked out in quarter-finals. But it's just a question of time."
The 28-year-old feels the same about himself. "I don't feel I must get past the quarter-final stage or not, because I know if I do the things right, I will do it.
"Doesn't matter this time, next time, or in couple of years anyway, because in the end, 10 quarter-finals I have. It's bigger than many players who did one or two semi-finals, and I will not replace those 10 quarter-finals for one or two semi-finals."
