The guest log is telling me to talk to the old man in the throne room, but he doesn't mention anything about the house. He just keeps saying "caution, caution, caution" --- That looks like something fat Steven Seagal would wear.
You need to help the Jarl with 2 quests. Once you finish the second one you can talk to the man at his right & he will give you the option to buy the house. I actually just did this yesterday. --- Nothing is true....Everything is permitted