The 26-year-old was told just over a week ago by new Cologne coach Stale Solbakken that Pedro Geromel will be his choice of club captain and not the fans' favourite Podolski.
While admitting his disappointment upon learning of the decision, Podolski will continue to give 100% for his hometown club and does not want to play anywhere else.
"I definitely never thought about leaving the club just because I am no longer the captain," he told Sport Bild magazine.
"My attitude and my identification with Cologne have obviously not changed at all."
Podolski was given the captaincy by former Cologne coach Frank Schafer last January only for Solbakken to prefer Geromel after a few weeks in his role.
However, the Germany striker does not appear to have taken the decision badly.
He was voted man of the match in last weekend's 3-0 cup victory over SC Wiedenbruck and created two goals for his strike partner Milivoje Novakovic.