With third seed Guillermo Coria and Juan Ignacio Chela already into the last eight, Nalbandian and Gaudio could match the feat achieved in Hamburg last year when four Argentines made it to the semi-finals.
However, Nalbandian faces a hard task against Safin, who is on fire after two successive five-set victories, while the unheralded Andreev, who trains in Spain, is a genuine threat to Gaudio on clay.
Whatever the results in those matches, Russia and Argentina have been the dominant countries at Roland Garros this year.
Three Russians have already advanced to the women's quarter-finals and two men would reach the same stage should Safin and Andreev win on Monday.
Three-times champion Gustavo Kuerten of Brazil will hope to confirm his fine form after his three-set victory over world number one Roger Federer when he meets solid Spaniard Feliciano Lopez.
Australian Lleyton Hewitt will try to make it to the last eight for only the second time at Roland Garros against Belgium's Xavier Malisse.
