I don't know of any commercial products, but two ideas occur to me.
You use some strong adhesive/double sided tape, combined with Velcro (you'd want a large patch, nit just a couple panels) or zip ties to attach the drive to the back of your display. This would probably work better with a 2.5" drive, but a 3.5" might be feasible if you had strong enough adhesive. The catch is that it whatever you stick to your display would most likely be permanent.
Alternatively, making/adapting some sort of shelf that attaches to the VESA mount point would probably work well. I'm thinking a metal bracket of some sort that would fit between the display bracket and mount, with a shelf at the top, to which you could zip tie or otherwise attach the drive, to allow for rotation. This would probably be more elegant and non-permanent, but you'd need to scrounge or be able to make the appropriate parts.