Designing Or Customizing A HDD/SSD Logic Controller
Rotating drive? No. The manufacturing issues are too hard to overcome.

Solid state drive? Yes, provided you have time and money; I'd ballpark it as a person-year hardware and software development plus a few thousand for manufacturing. You could probably get a beta version working with half of that by starting from an existing development board (FPGA or some of the faster SOCs) with a SATA slave or PCIe interface. Essentially there are four parts:


controller to host PC interface. Write software or HDL; some of this may be available as IP already.
controller to Flash interface. This is standardised, but you'll have to implement wear levelling and error correction on top of it.
firmware and board housekeeping. All the other stuff like power supplies and bootup sequence.
board layout and manufacturing if you're doing your own board.


It's within the range of a bright graduate who has access to occasional guidance.