Yes - I know people who would consider it inappropriate and unprofessional to ask for a reference in the situation you described. Personally, I'm flexible, but I would still recommend a different approach that will provide better results.
Instead of asking for a reference, it is better to ask for feedback on your performance at your current job.
You represent your company when working with this person. Explaining that you are looking for a new job and asking them to serve as a reference could be considered unprofessional. It might also cause problems if you make them feel awkward or if they decide to mention your job search to someone else at your company, like your boss. Plus, you run the risk of sounding like you're complaining about your current job or the company you work for, which would make things even worse.
However, asking for feedback on your performance is great customer service; after all, everyone you work with is a customer in some sense.
Ask specific questions when you approach them about things related to your work together. Focus on questions that highlight skills that you value and want to promote, but also focus on finding out if there are ways in which you (or your organization) could better serve their needs. You're trying to ask for honest feedback on your performance.
Be prepared for criticism. There is going to be a lot of opportunity for growth early in your career, so they may have a lot of feedback. You may not like what you hear though, so try to remember that quality feedback is actually very valuable; why would you want to waste time making mistakes when you can listen and learn from anyone who cares enough to share their opinion and help you out.
Try to get feedback in writing. And if things are going well, request a Recommendation through LinkedIn. The recommendations on LinkedIn will become part of your professional profile, which is something you can definitely refer prospective employers to.
Finally, if for some reason you feel that you are close enough to trust this person and you still want to ask them to serve as a reference, keep it positive and avoid complaining or being negative at all. If they ask why you are asking for a reference, just explain while you are happy in your current position, a new and exciting opportunity has come up that you would like their help pursuing.
ps. I am okay if you down vote my answer, but feedback on why you are down voting is useful and appreciated.