I must say the a year ago has been unbelievable for him... "Winning these type of matches against a top 10 player like "Sascha" is a gift", he said.
Medvedev awaits Federer after the Russian 13th seed prevailed 7-6 (7-5) 6-7 (5-7) 7-6 (7-0) over Reilly Opelka.
The world No. 5 produced an excellent all-round performance in dispatching Serbia's Filip Krajinovic 7-5, 6-3 on Monday, despite being tested by the world No. 103 during an exciting first set.
"I felt all the important points, points that could have led to something interesting for me, I played poorly because I was in two minds".
Federer began to pressurise the Albot backhand and eventually it brought him some joy, a wayward shot beyond the baseline bringing a break and set point, a cushioned volley at the net converting to level the match.
A little lucky and really good, Federer won 7-5, 6-3 Monday to reach the fourth round.
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South Africa's Kevin Anderson continued his return from an arm injury with a 6-4 7-6 (8-6) win over Joao Sousa of Portugal. After more than two months away from the court with an elbow injury, the world number seven smashed 17 aces en route to the second round win over the 21-year-old Munar. "Three years ago I got injured. But I still kept going after them, and I was able to hit my spots and keep the pressure on and shorten points as the match went on", the Association of Tennis Professionals (ATP) quoted Federer as saying.
"I'm looking forward to the game", Federer said of Medvedev.
Petra Kvitova booked her place in the last eight.
Eighth seed Stefanos Tsitsipas easily beat Mackenzie McDonald 7-6 (4) 6-1.
Kvitova, a two-time Wimbledon champion, is ranked a career-high No. 2 and will rise to No. 1 if she wins the title.