Eriksson has been linked with the available job as Portsmouth manager in recent days.
But the Swede intends to lead them in the 2010 World Cup, despite coming under increasing pressure.
“Why I will continue? Because I still have a running contract and I think that I would be a man without courage if I quit now,” Eriksson said.
“We are in a difficult moment because we are not winning away and we are not scoring, but I want to start winning away and take Mexico to the World Cup. I trust Mexico will be in the World Cup.
“We want to win the stage and qualify. We’ll keep working. I would not be brave enough if I said: ‘Thank you and goodbye’.”