Liverpool's American owners Fenway Sports Group have no plans to travel to the UK and, at this stage, plan to oversee the recruitment process from the United States.
Although talks have been positive, an appointment is not imminent.
Klopp is understood to have spoken to former Liverpool and Germany midfielder Dietmar Hamann about the club, the city and the fans.
He has been out of work since leaving Dortmund, with whom he won two German Bundesliga titles, in the summer.