Earlier this month, the U.S. Department of the Treasury's Office of Foreign Assets Control designated Marquez as a front person for alleged cartel leader Raul Flores Hernandez, freezing the defender's assets and prohibiting U.S. citizens from doing business with him.
Marquez hasn't played since for his club, Atlas, and has remained quiet since issuing a denial and vowing to fight the designation.
Mexico coach Juan Carlos Osorio said Thursday that he hasn't yet spoken to Marquez but is looking forward to sitting down with the 38-year-old to hear his side of the story.
"I’m sure I’m going to have a great chance to chat personally with Rafael and express to him, well first to listen and second to express our opinion," Osorio said at a news conference to announce the squad. "We all know it’s a difficult situation and we can only hope it gets resolved in the best way possible."
Marquez had hoped to join the likes of Lothar Matthaus and countryman Antonio Carbajal in playing at a fifth World Cup but, despite not being charged with a crime, may see that dream end with the OAFC's designation.