Given that you say it is highly probable you are offered a job after your internship then I would recommend you waited for them to do the offer, to avoid as much as possible being taken as too demanding.
However there is nothing wrong in asking. Seems that you are performing well at your position (evidenced by the high chance of being offered a job and your willingness to take it). If you do ask, remember to convey your enthusiast and interest in the company and job, and that you have found it a great fit for you. Also, do it when you see it is more convenient (i.e.: no incoming critical deadlines, or no stressful week), and again I would wait as much as possible before asking myself (maybe 3+ months is a bit earlier, try to wait at least 1 month before).
Besides asking the best you can do to ensure that you will indeed be offered the job is to maintain an excellent performance and attitude. Nothing speaks better than actions when trying to convince someone. If you have not, try giving "the extra mile" in your tasks now and then, so they can see you are indeed interested beyond just monetary compensation. Also, remember to be polite and respectful to all your coworkers, and not only those you relate to or your immediate superiors; you should treat the janitor with the same respect you should give to anyone else. That is an exemplary attitude and a sign of someone humble and willing to learn.
Just remember, be careful you are not doing this "just to land the job", and as soon as you get it stop being exemplary. Any experienced manager will easily see that you are faking it just to get the job; your attitude should be genuine and that is the tough (rewarding) part of this. However, this is easily achieved if you and the company/job are a good fit to each other, as things tend to flow naturally plus you enjoy it. I hope this is you case and that these words help you get the job, good luck.