Podolski's contract at his boyhood side runs out at the end of next season, which has put the prolific German striker in frame for plenty of transfer speculation in the recent months.
The 26-year-old has been heavily linked with Arsenal and Lazio recently, with speculation suggesting that the clubs may even attempt to sign Podolski in January.
However, Horstmann still believes that there is every chance that Podolski could decide to sign a new deal with his hometown club.
He told Kolner Stadt-Anzeiger: "The fundamentals are clear: Podolski has a year-and-a-half left on his contract and we want to go into the talks at an early stage - with the aim of extending this contract.
"For Podolski, I'm optimistic that we have the chance [to re-sign him]."
Horstmann believes that Podolski being rumoured to be are at odds with Cologne's director of sport Volker Finke will not be in the way of the striker resigning a contract.
"The two don't have to love each other but they must respect each other and trust each other," he said, "and I have the impression that this is the case."
Podolski has been key to Cologne this season, scoring 14 goals in 16 appearances in the Bundesliga.