Klose is currently second behind Muller with 62 goals, and needs only six more goals to equal the record.
The 33-year-old is currently in red-hot form after leaving Bayern Munich in the summer. He has scored five goals from seven games thus far in the season.
With the national team facing Turkey and Belgium in the upcoming international fixtures, Klose hopes to close in on the record.
He told Bild: "I want to break the record with the national team now,"
"We want to win all 10 qualifying matches, and then I will speak with the coach about my future.
"I am a spontaneous person, and I will make my decision about when I retire from a gut feeling. But for as long as I am enjoying myself and am free of injury, then I want to keep playing.
"I never fear competition. It is all down to me anyway - when I am fit, I will play. And I am feeling really good."
Germany have already qualified for Euro 2012, but will travel to play Turkey on October 7 before hosting Belgium four days later.