The 36-year-old equalled the 15 goals scored by Brazil legend Ronaldo when he found the net in die Nationalelf's 2-2 draw with Ghana in Fortaleza on Saturday.
Klose, who also became only the third player to score in four different editions of the tournament, insists he is ready to take the record and is keen to do so as soon as possible.
"I am very happy with my 15th World Cup goal, but I will wait to set the new record in the next game," the Lazio forward told RAI Sport.
"Now our minds are on the USA, as we want to win and go through to the next round. Of course I’d prefer to come on with my team in the lead, but there was huge tension and Ghana played very well.
"I always accept the decisions of the coach," he added when asked about not starting the Group G clash.
Upon reaching the goal-scoring milestone Klose was also congratulated by Ronaldo, who took to social media to pass on his regards to the German.
"Welcome to the club," the 37-year-old Brazilian wrote on Twitter.
"I can only imagine your happiness!!! What a great World Cup!!!"