This is leaning on the pleasure centers in your brain. It's nice to have attention paid to you, particularly by someone attractive who is in a position of power.
Now look at it objectively. He is the boss and you are a new employee. Does he spend time with other new employees? Spending extra time with the new hire is kind of typical in an office situation.
But let's say he's into you, the whole nine yards. Then this is a horrible position for you to be in. Not only can it turn sour if you put your foot down (even subtly, e. g. you walk in one day with an engagement ring on), it can also potentially turn into office grapevine material. Because, you see, a lot of folks don't like it when it seems like someone gets a promotion or a raise, or dodges a layoff bullet, because they're cute and not because they're at all competent.
Consider talking to HR about getting a mentor in the company from outside of your department. You will have every reason to hang with them (so long as your work is getting done) and your boss will not have a reason to mentor or fake mentor you anymore. This can also be a person you can confide in if it turns into more full-blown flirting/harassment, and they can possibly be your reference if this guy refuses.
Seriously consider putting out feelers to find a different job, too. These flirtations always look cute in the movies, but the person who gets screwed is inevitably the one who is lower in the corporate food chain and that person is nearly always younger and is often female.
Don't become a victim.