The parties - the association's chairman, vice chairman and Klopp - met on Friday for a first in-depth meeting.
"During the constructive talks, the parties reached an agreement on the most important points of a potential contract," the association writes on its website.
Negotiations between the federation and the 59-year-old German will continue next week.
When Julian Nagelsmann left the men's national team after the World Cup fiasco, Klopp was mentioned as the heir to the job.
Klopp - who was a popular coach at Liverpool for nine years until 2024 - would then leave his job as football director for the Red Bull Group.
