The Germany international believes that the club should be allowed to move on given the midfielder has already apologised for his behaviour during a taxi ride in Dusseldorf
Peszko was detained by police because of his allegedly drunk and disorderly behaviour during a taxi ride in Dusseldorf on Saturday night and has, according to the Kolner Express, already been fined and dropped from Stale Solbakken's squad for Tuesday night's Bundesliga clash with Mainz.
Podolski, though, would hate to see Peszko axed by Poland for their Euro 2012 campaign and does not want to see the incident distract Koln from their bid to avoid relegation either.
"It does no good to pull the team and the whole club into the dirt," the Germany international argued.
"If we are to stay in the Bundesliga, we need to keep our concentration, that has to be the goal. FCK should remain first class.
"And I hope that Slavo still gets to go to the Euros. It is his dream and he is important for the Polish team.
"Peszko apologised. He never caused anyone harm. I think you should change the topic now."
However, Poland coach Francizsek Smuda has been left enraged and bewildered by Peszko's antics.
"I have forgiven him once before for a similar escapade," he revealed. "This is inexcusable and reflects badly on all Polish players, even those with Borussia Dortmund."
Meanwhile, Koln coach Stale Solbakken is also fuming over the nature of the incident.
"Slavo will obviously not be there against Mainz [on Tuesday night]," he revealed. "I must be able to trust my players. What he has done is unacceptable."
The 27-year-old Peszko joined Koln from Lech Poznan in January of last year.