Karius quit his loan with Besiktas this week citing unpaid wages for the reason.
The former Mainz No1 is not required at Liverpool for next season and has been encouraged to find himself a new club.
Sabah reports Karius has already reached personal terms with Hertha Berlin.
Hertha chief Michael Preetz was coy about the reports yesterday, though refused to deny the claims.
He said, "We do not generally comment on such rumours. We would like to keep it that way."