Klose thrilled with first six months at Lazio
He's scored nine goals in 15 games plus two in five Europa League appearances.
"I am truly happy in Rome, as Lazio were what I had been looking for," said the 33-year-old.
"In this period I trained really hard and this is why I scored so many goals. I feel good psychologically and physically, while I get on perfectly with Coach Edy Reja.
"I don't want to give myself compliments, though, because I still really want to improve. If the fans have nicknamed me Kaiser than I'm happy, as such an important name means I'm doing well.
"Euro 2012 is the big objective I have in mind for next year, but it's not the only one."