After scoring twice in Germany's 4-0 demolition of Argentina on Saturday to help his team advance to the semi-finals, Klose, who won his 100th cap in the match, brought his personal World Cup tally to 14 goals in three tournaments, level with Germany's Gerd Mueller.
"If it was up to me I would prefer to win the World Cup than top the World Cup scorers' list," the soft-spoken forward told reporters, a smile barely visible on his face as his joyous team mates shuffled by him holding empty beer cans.
"Of course it is a compliment to be up there with Gerd Mueller but I want the World Cup," said Klose, who has scored 52 goals for Germany.
He was quick to note Mueller had scored his 14 goals in two tournaments.
"This is my third World Cup, so it is not a fair comparison," he said.
TIMING
Klose played in the 2002 World Cup final, when Germany lost to Brazil, and made it to the last four of the 2006 World Cup before his team bowed to eventual champions Italy.
"Today it was all about timing. I think our timing was perfect, striking at the right time," he said.
"I am delighted we have been given the right to play two more games (semi-final and final, or third place play-off). We just have to wait and see what will happen," he added.
Klose went into his third World Cup on the back of his worst season, having scored just three goals for Bayern Munich.
But he has already scored four goals in just four games here, as he missed Germany's final Group D match to Ghana through suspension.
"I always knew that I could score goals," he said.
Germany's Klose hints at international retirement
Serbia stun 10-man Germany
Defender Beck dropped from Germany squad
Will give appropriate reply at right time: Arjun
Mueller is new Mister Goal, says Gerd Mueller