The Spaniard will square off against compatriot Carlos Alcaraz while the World No. 1 will face 12th seed Hubert Hurkacz.
Reigning champion Alexander Zverev will take on Felix Auger-Aliassime while Stefanos Tsitsipas will lock horns with Andrey Rublev. All four matches promise to be tense affairs and it's anyone's guess who will make the final four.
Let's take a look at the odds and predictions for all the quarterfinal matches on Day 6 of the Madrid Open.
Novak Djokovic (-350) vs Hubert Hurkacz (+270)
World No. 1 Novak Djokovic reached the quarterfinals via a walkover after Andy Murray withdrew from their third-round encounter due to illness. He will now take on an in-form Hubert Hurkacz, who beat Dusan Lajovic 7-5, 6-3 in his last-16 encounter.
Djokovic was dominant in his second-round win over Gael Monfils, but his match against Hurkacz will give us a fair idea of where his game is at the moment. The two players will meet for the fourth time, with the Serb having won each of their past three meetings.
The match may play out in the same manner as the pair's meeting at the Paris Masters last year, where Djokovic held his nerve to prevail in a third-set tie-break.
Pick: Novak Djokovic to win in three sets (+310) via Oddschecker.
Rafael Nadal (-115) vs Carlos Alcaraz (-105)
Rafael Nadal vs Carlos Alcaraz was a match-up that many were hoping to witness once the draw for the Madrid Open was released.
Both players reached the quarterfinals after tough battles in the Round of 16. Nadal had to save four match points in his win over David Goffin while Alcaraz was victorious in a tight three-set encounter against Cameron Norrie.
This will be the third meeting between the two Spaniards, with Nadal leading the head-to-head 2-0. However, Alcaraz will fancy his chances this time around, especially considering the King of Clay is not at his best physically.
But Nadal should never be counted out and will be determined to advance further, especially since a potential semi-final meeting with Novak Djokovic awaits.
Pick: Rafael Nadal to win in three sets (+333) via Oddschecker.
Stefanos Tsitsipas (-250) vs Andrey Rublev (+190)
Tsitsipas and Rublev will clash in the last eight of the Madrid Open. The Greek is yet to drop a set in the competition, beating both Lucas Pouille and Grigor Dimitrov 6-3, 6-4.
Rublev, on the other hand, had to fight off Jack Draper and Dan Evans to reach the last eight. Both players have fared well this season, with the Russian having won three titles while Tsitsipas triumphed at the Monte-Carlo Masters.
This will be the ninth meeting between the two players, with the head-to-head locked at four apiece. Rublev won the pair's last encounter at the ATP Finals last year and will be hoping history repeats itself.
Pick: Andrey Rublev to win in three sets (+500) via Oddschecker.
Alexander Zverev (-200) vs Felix Auger-Aliassime (+162)
Zverev will look to keep his title defense alive in Madrid after a disappointing exit at the BMW Open, while Auger-Aliassime will be keen to maintain his strong run of form.
Zverev has been the better player between the two on clay but the Canadian cannot be written off.
The two players will meet for the seventh time, with Zverev leading the head-to-head 4-2. The match could go the distance, with Auger-Aliassime potentially edging out his German opponent.
Pick: Felix Auger-Aliassime to win in three sets (+500) via Oddschecker.