Despite stating that his client would not leave his hometown club in January, Schramm failed to dampen speculation linking the German forward with AC Milan.
"Milan? We don't comment on these rumours. There are a bunch of rumours on him, every day there are calls from Italy, from England and even from Russia," Schramm told Goal.com.
"The real truth is that Lukas has a contract with Koln and he is comfortable here. At the moment this is how things are."
Podolski, 26, has scored 14 goals in 16 Bundesliga appearances this season.