The Germany international moved to Lazio this summer after four years at Bayern Munich.
Klose has made an instant impression in Serie A, scoring four goals in six league appearances, including a late winner in Sunday's 2-1 triumph over Roma in the city derby.
"If everything goes well, I hope to play until 2014 with Lazio, appear in the World Cup and then end my career," Klose said to Kicker magazine.
Klose, 33, scored nine goals in qualifying to help Germany secure a spot in Euro 2012.
The veteran forward has struck a total of 62 goals in 112 appearances for Germany so far.