The Germany international was close to leaving the treble winners for Hoffenheim a few years ago after the current USA boss told him there was no room for him the first team
The Sinsheim side were keen to lure the Germany international away from Bayern ahead of the 2008-09 campaign and Klinsmann was happy to let go of the versatile attacker.
However, assistant coach Hermann Gerland advised against selling Muller and the transfer eventually fell through.
"Then coach Jurgen Klinsmann had made up his mind and told me that there was no room for me in the first team," Muller was quoted as saying by Kicker.
"Tiger Gerland did not want to sell me, though. Plus Hoffenheim's offer wasn't sufficient. The transfer window then closed and I stayed put. I now know that was the best outcome possible."
Muller, 23, broke into the first team in 2009-10 under Louis van Gaal and has since become a key player at the Bavarian giants.
Klinsmann moved on from running the Allianz Arena side and currently coaches USA, who beat Germany 4-3 in a friendly earlier in June.