Juventus midfielder Khedira is expected to leave the Serie A champions before the transfer window closes.
The contract extension the World Cup winner signed in 2018 is up at the end of the season, but he is set to depart early having failed to appear in a single matchday squad for Juve this term.
Khedira initially had a big impact after joining the Turin club in 2015, scoring 19 goals in 77 games across three successive title-winning Serie A campaigns.
He has since played just 22 times in the competition, suffering with injuries and falling out of favour entirely under rookie coach Andrea Pirlo.
Khedira spoke of a potential move to the Premier League ahead of January, but Berlin and Hertha – 14th in the Bundesliga – now appears his most likely destination.