The veteran striker's 33rd-minute goal against Austria on Friday has seen him draw level with the legendary Bayern Munich hitman on 68 international strikes
The 34-year-old has been a constant fixture for the Nationalelf since making his debut in 2001, appearing at three World Cups and as many European Championships.
On Friday, the Lazio frontman matched the legendary Bayern Munich striker's international record in his 129th appearance for his country with a 33rd-minute effort against Austria.
Muller scored his 68 goals for West Germany in just 62 appearances, helping his nation to the 1972 European Championship and the 1974 World Cup.
Klose, meanwhile, will be hoping to represent his country at Brazil 2014 as he sits one goal behind Selecao legend Ronaldo in the World Cup's all-time scoring charts, level with Muller on 14.