Klose, who helped his country win the 2014 World Cup and became the all-time top scorer at the tournament with 16 goals, ended his playing career last season at Lazio.
"He will undergoing an individual training and trainee programme with the clear aim of starting a coaching career," the FA said in a statement.
The 38-year-old, who also played for Kaiserslautern, Bayern Munich and Werder Bremen, is Germany's leading scorer with 71 goals in 137 matches.
"In the past months the thought has matured in me to remain on the pitch with the perspective of the coach," Klose said. "I would like to thank (Germany coach) Joachim Loew and (sports director) Hansi Flick for the chance to sharpen my perspective in a practical environment."
He will be part of Germany's coaching team for their World Cup qualifier in San Marino and a friendly against Italy this month.
(Reporting by Karolos Grohmann, editing by Ed Osmond)
