Ahead of Tuesday's friendly with Joachim Low's men at Wembley, England manager Hodgson told Bild am Sonntag he was approached by the German Football Association (DFB) 15 years ago.
However, former Germany player and manager Beckenbauer was not keen on an overseas appointment, and Erich Ribbeck was subsequently named as Berti Vogts' successor.
Discussing the contact from DFB president Egidius Braun, Hodgson, who was the boss of Blackburn Rovers at the time, said: "It was an honour when Braun called me.
"I was on the president's wish-list. He would have had problems convincing people to accept a foreign coach though.
"At the time, my friend Franz Beckenbauer pointed out that a foreign coach of the Germany national team would not have helped the German coaching programme - the up-and-coming coaches."
Although Ribbeck was 61 when appointed, Germany have gone on to appoint a trio of youthful coaches.
Rudi Voller and Jurgen Klinsmann were 40 and 39 respectively when they took charge, while current boss Low was 46 at the time of his appointment in 2006.
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