The 22-year-old has shown impressive form in the Bundesliga on loan from the Reds this season.
Hertha are trying to secure a European spot this season, with Grujic managing two goals in 10 appearances.
They want to hold onto him for another season, if possible.
"First and foremost, we're happy that we have Marko," Hertha sporting director Michael Preetz told Kicker.
"I'd always prefer that a player helps me out for a year than not at all. We'll certainly talk to Liverpool about the next season.
"All the guys can help us make a difference in a season when something extraordinary is possible.
"That is our goal, and it would be wonderful to successfully take the next step together."