He said he is leaving because he wanted to spend time with his family, who live in southern California.
Rummenigge also said Kahn had been devastated by the decision of Germany coach to relegate him to second put him on the bench behind Lehmann.
The former Germany goalkeeping trainer criticised coach Juergen Klinsmann for demoting Oliver Kahn and giving Jens Lehmann an equal shot at the position.
Franz Beckenbauer said Klinsmann should stay on as coach because the job he started rebuilding Germany football is not finished yet.
"We are hugely disappointed (but) you can only compliment the team, they're a young team. They made a whole country really proud," added Germany coach.
Juergen Klinsmann doused speculation he might be the next United States coach
Hungary coach Lothar Matthaeus believes Juergen Klinsmann has done a great job in his first five months in charge of the Germany team.
The former captain set winning the 2006 World Cup on home soil as his goal after officially taking charge of the national team.
Italian TV channel RAI Sport, where Rossi had been working as a pundit, said on Thursday "Pablito" had died of an "incurable disease".
Sunderland have given permission to the Football Association (FA) to speak to manager Sam Allardyce about the vacant England post, the Premier League club said on Wednesday.
A prolific striker in Germany's second division, Loew's first major coaching job was at VfB Stuttgart in 1996. After further stops at clubs in Turkey and Austria he joined Germany in 2004 as assistant coach.
Mexico's Oribe Peralta and Alex Morgan of the United States were named winners of the inaugural CONCACAF Male and Female Player of the Year awards on Friday.
Extends contract up to 2020
The draw for the eight groups for the final round of the 2014 FIFA World Cup, which will be played from June 12 to July 13 in Brazil, was just held in Costa do Saupe near Salvador de Bahia.
At the end of a World Cup in which Cristiano Ronaldo and Lionel Messi headed home after the first knockout round and Brazilian Neymar failed to deliver, the game perhaps needed a new talent to excite the global public.
Borussia Dortmund eased past nine-man Hamburg SV 3-0 to keep their slim Bundesliga title hopes alive on Sunday as they moved seven points behind leaders Bayern Munich with four games remaining.
Germany coach Joachim Loew will stay in his post despite his team's group stage elimination at the World Cup in Russia.