Assuming that you're speking to the right farmer (the only house with two farmers in front)...first you should respond by telling him to report it to militia because you have no time to chase some guy around, then he asks you again, and then your character is given the option to take the quest, he then adds, that the thief must live nearby...then you should have the quest added to your log. The thief is in the poor section (by the name Dorian), but don't turn him in, you'll get reputation bonus and IIRC more exp than you'd get by reporting him...sadly, he gets arrested anyway, and you can't help him.
I think you can break the quest if you go to the thief's cellar before you've acquired the quest from the farmer, I'm not sure, though, because I've never done it.