The Lazio strike surpassed Gerd Muller as his country's premier marksman by netting for the 69th time shortly after coming off the bench in a 6-1 win over Armenia in Mainz.
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Klose, though, claimed that while he is proud of the record, he just wants to get himself in shape for Brazil 2014.
"Of course the record means something to me," he told ZDF. "But it is much more important for me to become fit again.
"I didn't have the legs for the last friendly [against Cameroon]. Now they are coming back and it shows, I guess."
Germany had struggled during the first half of a friendly marred by an injury to Marco Reus just before the break and even when the host finally opened the scoring through Andre Schurrle, Armenia equalized with a Henrikh Mkhitaryan.
However, Joachim Low's side then cut loose, with Lukas Podolski, Benedikt Howedes, Klose and Mario Gotze all netting in the final 18 minutes.
"When the team plays as it did in the second half, I will get my opportunities and I will get my goals," Klose said. "It is important for us to push into the box - not play around it like some sort of handball team."