Pal Dardai's team, who just avoided the drop last season, have shown remarkable consistency this term under the Hungarian coach and occupy third position, three points clear of fourth-placed Schalke 04.
It is rare for Hertha to be so high in the table at this stage of the campaign and victory at home to 10th-placed Ingolstadt on Saturday would see them further tighten their grip.
Hertha, who have won three of their last four matches, could be excused for dreaming big and Dardai has urged his players to keep fighting.
The top three qualify for the Champions League group stages with the fourth-placed club advancing to the qualifying rounds.
"I am not a dreamer," said Dardai who turned 40 this week. "We all have wishes but for those wishes to come true we still need to work very hard.
"We have eight games left and we are gradually entering the crucial phase of the season so it is now that we need all the support of our fans."
Dardai, who played for Hertha for 14 seasons until 2011, has successfully injected a will to win into his side.
In their best season in recent memory, 2008-09, they missed out on the Champions League spot by one point.
Former Chelsea striker Salomon Kalou has hit top form in his second year at the club, leading the charge with 12 league goals, double last season's tally.
The 30-year-old Ivorian has found in Vedad Ibisevic the perfect partner, with the Bosnian rediscovering his poaching form with eight goals.
Hertha are unbeaten at home in their last eight matches at the Olympic Stadium.
"We have had a stunning season so far and now we want to gold-plate it," said captain Fabian Lustenberger. "We are fit, one unit and full of confidence."
Leaders Bayern Munich, five points clear at the top and buoyed by their midweek Champions League win over Juventus, visit Cologne on Saturday as they chase a record fourth straight league title.
Second-placed Borussia Dortmund travel to Augsburg on Sunday.
(Editing by Tony Jimenez)
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