The 35-year-old Serb is hot favourite to win a 10th Melbourne crown and with his hamstring seemingly recovered he will take some stopping.
He called his three-set mauling of Australian 22nd seed Alex de Minaur on Monday his best match of the year so far.
“Tonight, the way I played, the way I felt, gives me reason now to believe that I can go all the way,” he warned afterwards.
Djokovic is the only man left in a depleted draw to have won a Grand Slam before.
But even with his left hamstring much improved, Russian fifth seed Rublev will be no pushover.
The 25-year-old showed all his battling qualities to save two match points against talented Danish teenager Holger Rune in the last 16, scrapping his way to victory in five dogged sets.
“I know that Novak is a very tough player to beat, especially in the Slams,” said Rublev, who has never progressed beyond the quarter-finals at a Grand Slam.
“The only chance I have is if I play my best tennis, just fight for every ball, and that’s it. That’s the only chance.”
The other men’s quarter-final is an all-American affair between two unseeded players, Ben Shelton and Tommy Paul.
The 20-year-old Shelton is on his first trip outside the United States and is enjoying every minute of the ride.
“Each match that I’ve won here has felt the same — it’s a mixture of joy, relief,” said Shelton, who a year ago was at the University of Florida and ranked 569 in the world.
Now he is 89th.
“I just have that feeling of ecstasy. When the last ball lands, I did it. To be able to do that on this stage four times in a row, that feeling over and over again, has been pretty cool.”
The first semi-final has already been confirmed, with third seed Stefanos Tsitsipas facing Russian 18th seed Karen Khachanov.
In the women’s quarter-finals, Aryna Sabalenka will look to step up her title charge with a match against unseeded Donna Vekic of Croatia.
The women’s draw has also been decimated after a series of shocks and Sabalenka looks the clear favourite.
The fifth seed from Belarus is yet to drop a set as she zeroes in on a first Grand Slam title.
The other quarter-final on Wednesday is between former world number one Karolina Pliskova and unseeded Magda Linette of Poland.
Two-time Melbourne champion Victoria Azarenka will face Wimbledon winner Elena Rybakina in the semi-finals on Thursday.