Joachim Low's side completed their own group fixtures on Sunday by beating Denmark 2-1 to secure top spot in their section to set up a last-eight meeting with the Euro 2004 champions.
Klose is wary of the task at hand but believes Germany must remain true to their style if they are to overcome the Greeks.
“I am convinced we will have our chances, even if they will sit deep," Klose told Goal.com. "We have to play our game, then we will remain favourites and will win.”
The 34-year-old striker then went on to hail team-mate Lars Bender after his late goal against Denmark preserved the Mannschaft's 100 per cent record in the tournament.
Despite taking an early lead, Germany found themselves on equal terms with the Danes until the 80th minute when the Bayer Leverkusen midfielder, who was being deployed at right-back, netted the winner.
Klose admitted he is thrilled with how well his side are training together and the bond that is developing within the group.
“He [Bender] is a sensational guy,” Klose added.
“Everyone is giving their best, even the ones who don’t play. We have great guys in backup.
“It is fantastic to see how everyone is acting in training. Today [Sunday] you could see that we can put everyone in.”
Klose has found himself below Mario Gomez in the pecking order for Germany at Euro 2012, and he was granted just 15 minutes as a replacement for the Bayern Munich ace against the Danes.
Gomez is also confident ahead of his country’s final eight clash next week, but recognises there is a long way to go before they can reach the final.
"I'm just looking to my team and am happy that we are in the quarter-final,” Gomez said.
“We want to go to the final but it's a very long way to go."
Germany's last-eight clash with Greece is on Friday at 20:45CET.