I wouldn't put a hook on the shower door. It's too expensive and wouldn't want to put added stress on the hinges. You could put a clear Command hook on the glass wall, next to the door. They sell one for hanging wreaths on glass windows and front doors, so you can find them, this time of year, in the holiday aisle. This one has been on my south facing, front door in FL for about a year. I can't believe the blazing sun, and sideways rain hasn't loosened it.

Thank you for your ideas..

I agree draping the towel on th door would be easiest solution for now. I should actually do that if I cannot find any better solution.
Although this is the master bath, my kids would also use it occasionally. So I need to find a place for towel hanger or a towel hook else th towel would end on th tub or th floor.

The wall next to toilet has space just right for th toilet holder which is already installed.

I liked the command clear clip- by the way, I never heard of this. Thanks, for bringing this to my notice. I found this product in my local HD.
http://m.homedepot.com/p/Command-Mini-Clear-Hooks-with-Clear-Strips-6-Pack-17006CLR/203431547
My concern is-- can this clip hold heavy bath towels? And, is it strong enough to handle everyday wear n tear?

We use about a 2 inch suction cup with a hook on it inside of our shower to hold our bath towel. It has held up remarkably well and never falls off the wall. I like it because it is not noticeable at all

@ cooinkgistherapy That could be the solution for me too...can you please tell me what type of suction hook you used? Did you install it against the wall or glass?

@ tedbixby ... Good point on how fast towel can try. My shower is very new but there is a dry spot if I can get the hook on the fixed glass side inside the shower.

There are horizontal towel bar hangers in addition to towel hooks that can hang from the top of your door. If you used one of these on your bathroom door, it would not mar your door or interfere with the transparent look of your shower enclosure. Browse "over the door towel racks" to see multiple options.

We use the clear commando hook for our larger bath sheet size towels. It's been a year and the hook is holding us just fine. Good luck.

I used one of those decorative command hooks (large size in satin nickel) for my hair towel. I stuck it to an onyx/ cultured marble shower wall, and it's still holding fine. I like to have a towel the shower with me to wrap up my hair before I get out, and this has been the perfect solution.