According to Bild, the 27-year-old forward has no future at Hertha and is likely to move on in January with six months of his contract left.
Selke has so far scored two goals in 14 games for Hertha during the current Bundesliga campaign.
The Bild report suggests - Köln may be interested in securing the services of Selke, due to the fact that both Sargis Adamyan and Steffen Tigges combined have only scored four goals for them.
Plus, with both Sebastian Andersson and Florian Dietz being out with long-term injuries, Selke is seen as a 'quick fix' option.
Scottish Premier League side Rangers was keen on signing Selke last summer but were turned down by the player to stay at Hertha.
But now with the forward likely to look for a move in January, Rangers could also become an option for the player in ending their goalscoring woes of late.