EPA/ANDRE PICHETTESloane Stephens of the U.S. in action against Caroline Wozniacki of Denmark during the semi-finals of the Rogers Cup Women's Tennis tournament in Toronto, Canada, 12 August 2017. "Probably playing more ATP (tournaments), fewer Challengers".
It will be just the second career meeting between the two. Federer has won 15 straight matches on hard court.
Federer's performance was also buoyed by strong serve-and-volley stylings.
Federer said he goes out to win every match he plays, but admitted there were times when he felt sorry for his opponents.
'This is how I want to play for the whole week. "I was more committed and a step further in, adjusting my position slightly realizing the ball does fly a lot", Federer was quoted as saying on the ATP World Tour's Web site.
These two played once in the past, which was in the 2012 Davis Cup, a match Federer won in three sets.
Murray has withdrawn from Cincinnati with a lingering hip injury.
What's in a name: Denis Shapovalov gives an English pronunciation to his first name and he was asked how he feels about fans this week using the French version.
Ferrer took the first set 6-4 against world number three, who had not dropped a set since his shock defeat to Tommy Haas at the Mercedes Cup in June.
Other quarter-finals later Friday have Denis Shapovalov of Richmond Hill, Ont., against Adrian Mannarino of France and fourth-seeded Alexander Zverev of Germany against South African Kevin Anderson.
The 36-year-old Federer was on Thursday outplayed from the baseline in the early going by the unseeded Ferrer, who broke the 19-time Grand Slam champion's serve twice in taking the first set, reports Efe.
No. 6 Caroline Wozniacki def. Halep defeated Garcia 6-4, 6-2.
During the second set, immediately following a 12-minute rain delay at 2-2, Shapovalov broke at love.
Federer has an opportunity to regain his World No.1 ranking. "It's tough to come back and play that same level".
However, she wasn't fazed this time around. I came from vacation, did some fitness, saw how I was feeling and said, 'You know what, I practiced so much the previous year, let's go play some matches'.
Upsets, it turned out, were in style Friday. Federer has now won 10 of his last 11 sets played and is coming off a match in which he won 76 percent of his total serve points.
For large spells of the match, the Swiss appeared unusually frustrated, as his first serve dwindled and his much-improved backhand regularly misfired.