Second seed Murray is bidding to move ahead of Fred Perry, who was a five-time quarter-finalist, for the most Roland Garros last-eights reached by a British man with six.
Isner, the 15th seed, is aiming to become the first American man to reach the last-eight since Andre Agassi in 2003.
Murray has won all of the pair's five meetings but they have never met on clay.
"He generally doesn't play that deep on his returns," said Isner, the last American man in the tournament.
Andy Murray in action at French Open. Getty Images
"He takes the ball early. Against me, he stands in the court and sort of blocks it back. He has such great hands."
Third seed and defending champion Stan Wawrinka goes up against Serbian 22nd seed Viktor Troicki also boasting a dominant record at 4-0.
In those meetings, Troicki has taken just one set off the Swiss.
But Troicki has plenty of incentive to see off the champion as he has yet to reach the quarter-finals of a Grand Slam.
Japanese fifth seed Kei Nishikori has a 6-2 record over French ninth seed Richard Gasquet ahead of their last-16 tie.
Two of those wins came during the European claycourt swing this year in Madrid and Rome and both in straight sets.
Nishikori is trying to make the last-eight in Paris for the second successive year while Gasquet, the last French player remaining in either the men's or women's singles, has yet to reach the quarter-finals.
In the women's fourth round, Polish second seed Agnieszka Radwanska takes on 2010 Wimbledon semi-finalist Tsvetana Pironkova, the world number 102 from Bulgaria.
Radwanska has a 9-2 career stranglehold on the 28-year-old who has reached the fourth round in Paris for the first time.
But Pironkova has already knocked out two seeds on her way to the last-16 -- Sara Errani and Sloane Stephens.
Garbine Muguruza, the Spanish fourth seed, is looking to make the quarter-finals for the third year running.
She faces 2009 champion Svetlana Kuznetsova who won the pair's only previous meeting in Madrid on clay in 2015.
The day's other quarter-finals see Romanian sixth seed Simona Halep, the 2014 runner-up, against 2010 finalist Samantha Stosur of Australia.
Unseeded American Shelby Rogers faces Romanian 25th seed Irina-Camelia Begu.
Court Philippe Chatrier (0900GMT/1100 local)
Svetlana Kuznetsova (RUS x13) v Garbine Muguruza (ESP x4)
Viktor Troicki (SRB x22) v Stan Wawrinka (SUI x3)
Kei Nishikori (JPN x5) v Richard Gasquet (FRA x9)
Simona Halep (ROM x6) v Samantha Stosur (AUS x21)
Court Suzanne Lenglen (0900GMT/1100 local)
Milos Raonic (CAN x8) v Albert Ramos-Vinolas (ESP)
Irina-Camelia Begu (ROM x25) v Shelby Rogers (USA)
John Isner (USA x15) v Andy Murray (GBR x2)
Tsvetana Pironkova (BUL) v Agnieszka Radwanska (POL x2)
Updated Date: May 30, 2016 13:33 PM