The iconic former West Germany striker insists that he hopes the Lazio frontman surpasses his goalscoring tally.
The Lazio attacker, 34, is one goal shy of equaling the tally of 68 set by the Bayern Munich icon, which has stood for 39 years.
Ahead of Germany's friendly with USA - which is coached by another former Germany striker, Jurgen Klinsmann - this weekend, Muller praised Klose's character and insisted that his compatriot has earned the accolade.
"It has long since just been a matter of time before he breaks my record. I am pleased for him," the 67-year-old known as der Bomber told SID.
"Miro is a great striker and a great guy, who I met a few times when he played for Bayern Munich. He's deserved it."
Joachim Low's men head into the friendly with Klinsmann's side on the back of a 4-2 win over Ecuador, in which Lukas Podolski scored after just nine seconds.
Klose joined up with the Mannschaft squad after the Biancocelesti's Coppa Italia win on Sunday and is expected to feature in the USA clash.