British seventh seed Murray defeated Spain's Fernando Verdasco 6-4, 7-5, 7-6 (7/3) to reach the quarter-finals for the fourth time.
Wimbledon champion Murray, whose best run in Paris was a semi-final spot in 2011, will face French 23rd seed Monfils after extending his record over Verdasco to 10-1.
"I'm looking forward to the next match with Gael, it should be a great atmosphere," said Murray of a rivalry which began when the two were children playing in Les Petits As tournament in the French town of Tarbres.
"I first played Gael when I was 10 and he was 11. He's an unbelievable entertainer and fun to watch," said Murray.
"He's a great athlete and a nice guy. It should be a tough match but with some fun points because of the way we both play."
Monfils reached his fourth Roland Garros quarter-final with a 6-0, 6-2, 7-5 win over unseeded Spaniard Guillermo Garcia-Lopez, the man who put out third-seeded Australian Open champion Stan Wawrinka.
Monfils, 27, who made the semi-finals in 2008, trails Murray 3-2 in their senior careers but the pair have not met since 2010 when the flamboyant French player won at the Paris Masters.
The Frenchman also came out on top in the first round of the 2006 French Open in five sets.
"I think Andy has changed. He won Wimbledon, he's a good player. After his back injury he is more solid. He's proved on clay that he's also a tough opponent."
Source: AFP
