How can I add a door to my basement?

So the problem that we have is that the previous homeowners built on a mud room to the back of our home and the door to the basement no longer fit. So they just put up a make-shift door with no frame and used a baby lock device to keep it shut. The issue I'm having is that the opening for the door is only 68 in high and immediately starts going down at a 45 degree angle so there is no room for a door frame inside the current opening. I don't mind building out slightly but would hate for it to be more than an inch or 2 build out. I'm tired of how awful the door looks, but I'm lost for how to fix it. Any advise would be so greatly appreciated!