Podolski joined Arsenal from Cologne in June 2012, but has been frustrated by his lack of starting opportunities since the arrival of Alexis Sanchez from Barcelona in the close season.
The Germany international and World Cup winner has hinted that he may have to leave the Emirates Stadium to secure more first-team football, although manager Arsene Wenger has since denied that the 29-year-old is in line for a move away from the club.
And Cologne sporting director Jorg Schmadkte has poured cold water on suggestions that a switch back to the RheinEnergieStadion could be on the cards.
"We've explained our standpoint, and I think that Lukas also sees it that way," Schmadkte told Bild.
"We don't have five million euros, and we can neither pay the transfer fee nor the salary of a player like Podolski."
Cologne president Werner Spinner also dismissed talk of an approach for the former Bayern Munich man, expressing concerns that Podolski's return could disrupt the harmony of the squad.
"It would be difficult to integrate a national team player who has 121 caps and also plays Champions League at Arsenal," Spinner said.
"But nobody in Cologne has anything against Lukas Podolski. He is a popular figure, but we don't want to put the squad and their homogeneity in danger."
‘After Manchester City’s recent form, maybe they’re the underdogs against Manchester United!’ Former Red Devils defender on this weekend’s derby
‘Arteta, Alonso, Emery, me… none of us were physical players – we needed the understanding of the game. That probably helped us move into management’: Premier League boss reveals reasons for natural career progression
