Top-ranked Djokovic stretched his Grand Slam win streak to 26 matches by eliminating sixth seed Berrettini 5-7, 6-2, 6-2, 6-3 at Arthur Ashe Stadium in a rematch of July's Wimbledon final
World number one Djokovic rallied past 99th-ranked Brooksby 1-6, 6-3, 6-2, 6-2 to book a quarter-final encounter with Italian sixth seed Matteo Berrettini in a rematch of July's Wimbledon final
Medvedev defeated British 24th seed Daniel Evans 6-3, 6-4, 6-3, making his fourth trip to the last eight in the past five Grand Slams as he chases his first Slam title
Djokovic has already owned all four Slam titles at once after winning the 2016 French Open and said that was the moment he felt a calendar Slam was possible
The 34-year-old Serbian star dominated much of the way in beating 18-year-old Danish qualifier Holger Rune 6-1, 6-7 (5/7), 6-2, 6-1 after two hours and 15 minutes in the night feature at Arthur Ashe Stadium
Djokovic is playing in his 10th semi-final at Wimbledon and 41st at the majors while his progress at the event has comfortably taken his career earnings past the $150 million mark.
Two-time champion Andy Murray, whose ranking has slipped to 118 as he battles to come back from hip surgery, will be aiming to win gold for the third Olympics in succession.
Djokovic insists there will be no letdown physically or emotionally after reaching the final in Paris for a sixth time with an epic triumph over 13-time champion Nadal.