Marquez backs Herrera to stay
Herrera has negotiated his side through a tricky Group B that featured Brazil, Croatia and Cameroon, having picked up seven points from three outings.
Mexico will come up against the Netherlands in the last 16 as they look to make it into the quarter-finals for the first time since 1986 on home soil.
Marquez wants Herrera to carry on in the role he first undertook late last year - having steadied the ship during his relatively short time in charge by guiding them to Brazil.
Asked by ESPN Deportes whether he thought Herrera should continue, Marquez responded: "Yes, I do, but I think now we have to focus on what's coming.
"(The Netherlands) are a huge team and, yes, they are a huge favourite.
"We are (doing) well and have done things well. Those who are substitutes are giving everything to try be in the team."
Former Mexico defender Herrera is currently in his first international management job, having previously taken charge of domestic sides in the country.