Second seed Federer, who beat world number one Novak Djokovic in the Cincinnati final and is striving to add to his record 17 grand slam singles titles, plays 34th-ranked Leonardo Mayer of Argentina.
Third seeded Murray, who defeated Djokovic in the Montreal final, faces number 37 Nick Kyrgios, the talented 20-year-old Australian who is on ATP probation after making a crude personal remark to Stan Wawrinka on court in Montreal.
Federer has been brandishing an aggressive style of play, forcing the action and rushing in to half-volley weak second serves to forge an advantage.
"My game is going very well. My volleying has been very good lately and very proactive going forward and I think my serve has been unbelievable lately," said Federer.
Federer, 34, who won five consecutive U.S. Open titles from 2004 but has not been back to the finals since 2009, holds Mayer in high regard.
"I didn't know he was unseeded. Total shock for me to see I was going to play him," Federer said. "It's really tough to be playing Leonardo Mayer."
Federer narrowly won their only previous meeting 7-5 3-6 7-6(7) last year in the second round of the Shanghai ATP Masters.
"The Shanghai match was one of the toughest ones I've ever won in my career," Federer said. "I like the power he has plus the serve, which makes him tough to control from the baseline.
"He's a challenge."
Murray eliminated Kyrgios from the Australian and French Open this year in straight sets and holds a 4-0 mark against him, but the Scotsman respects the firepower of the mercurial 20 year old.
Kyrgios faces a 28-day suspension and $25,000 fine if he steps out of line at an ATP event in the next six months, but the International Tennis Federation has said he would not be under such restrictions at the grand slam, which it runs.
Murray said he did not expect Kyrgios to be affected by all the negative attention.
"To be honest, I believe he likes playing on big stages. I would expect him to be ready for the match. He gets fired up for big matches," said Murray.
"Every match is a new match. He's quite an unpredictable player."Murray said he had some sympathy for Kyrgios, who has been harshly criticized since his slur against Wawrinka and the Swiss player's girlfriend, Croatian teenager Donna Vekic.
"He's a young guy," Murray said. "He made a mistake. All the guys here when they were 19 or 20 made mistakes. His was seen by millions. It's unfortunate it happened. It was wrong."
(Editing by Andrew Both)
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