The 34-year-old arrived from West Ham in January and helped the Light Blues to CIS Insurance Cup and Scottish Cup final victories as well as a UEFA Cup final appearance, where they lost to Russian club Zenit St Petersburg.
Dailly, who is in the Scotland squad for the friendly against the Czech Republic in Prague on Friday said: "I have spoken to the manager (Walter Smith) already and we have more or less agreed to do it again next season.
"I haven't spoken to the chief executive (Martin Bain) or anything like that and I haven't signed anything but in principle there is a good chance of me signing again for next season."