I need to clear up a few things
Him focusing on saving up money for his own house/car is understandable, but it has nothing to do with being in a relationship, the two are not mutually exclusive. So, I feel that this is a bunch of BS he's feeding you here, it could be he already has a long term partner/is cheating on her, it could be he's got commitment issues and is using that as a excuse as to why he shouldn't dive into things.
"Should I wait for him to ask me out", what world are you living in? No normal adult asks someone "will you be my girlfriend", that's something that is done in public and high school, not something somone in their 20's/30's would do. Not sure why you would say that, but you really need to get with the program here, and understand this doesn't happen in the real world.
I think its time you just confront him and let him know where you stand, and let him know you won't be his "toy" while he decides what he wants out of life! You need to grow some self respect and not be someone's "maybe" or "sloppy seconds. So its a matter of he either fully commits to you OR you guys go your seperate ways, there is no in between, and that you won't settle for less than you deserve.