I would like to buy Breezehome but when I talk to Proventus (the guy who sells it to you), he doesn't say anything about Breezehome.
You must first retrieve the tablet from Bleak Falls Barrow. Then, Proventus should give you the option to buy Breezehome for 5000 gold, and furniture for extra money. P.S. To get the house for free, push Proventus toward the cabinet on the left side of the room. As soon as you ask to buy the house, put all of your money into it. It will be yours for no cost.