Federer, the tournament's top seed and defending champion, swept through the first set against Adrian Mannarino of France in just 16 minutes, allowing only five points in the six games.
The 36-year-old is also on a streak of 32 consecutive sets won at the tournament, just two off his record.
Like his great rival Federer, Nadal has cruised through to the last eight without dropping a set.
By contrast, eight-time champion Federer, and Nadal, the title victor on two occasions, have played exclusively on the 15,000-seater Centre Court.
"I was then able to put away a good Mannarino - because, in the beginning, he didn't play very well but also, for me, I didn't miss much". Facing Roger again [would] be something fantastic. If you ask me if I prefer another (opponent), I say yes. "That's the point. It's about being smart, no?"
Novak Djokovic is Nishikori's next challenge after the three-time champion thumped Russian world number 40 Karen Khachanov 6-4 6-2 6-2 in an ominous display. "I will try to hold my service games most of the time".
Later Monday, two-time champion Rafael Nadal attempts to make the quarterfinals for the first time since he finished runner-up in 2011.
Tendulkar, Tendulkar, the former India captain widely renown as one of the greatest batsmen of all time, was impressed by Federer's form after the 20-time Grand Slam champion was spotted praticising his forward defence during his victory over Adrian Mannarino at Wimbledon.More news: Kane: We don't want to go home yet
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Alexander Zverev, who was 11 years old at the time, said: 'Of course I remember it.
"I didn't think that was ever going to happen, to be honest."It's a very positive four matches for me. His problem has always been the first week of Wimbledon, not the second week.
Anderson, who reached his first Grand Slam final at the 2017 US Open, had lost in the fourth round at Wimbledon on three previous occasions.
He will play South African eighth seed Kevin Anderson or France's Gael Monfils in the last eight on Wednesday.
The 12th seed faces Kei Nishikori on Wednesday ahead of a possible semi-final with Nadal and Murray on Tuesday talked up the possibility of Djokovic pulling off what would be a significant upset by taking the crown.
The All England Club has come under increasing pressure to rethink its 2pm (1300GMT) start time for Sunday's men's singles final with the football showpiece in Moscow kicking off at 4pm in the United Kingdom (1500GMT).
Juan Martin del Potro advanced to the Wimbledon quarterfinals for the first time since 2013 by beating Gilles Simon 7-6 (1), 7-6 (5), 5-7, 7-6 (5).
Del Potro was leading Simon two sets to one - 7-6 (7-1) 7-6 (7-5) 5-7 - when their fourth-round match was suspended under fading light.