What does your contract say? If you’re not in a development role at your current company, I suspect it will only talk about soliciting customers away or staff.

You’d need to build it in your own time and on your own hardware of course.

I’d personally be up front with them that you’re working on it, get a letter from your boss too - purely as a just in case.

If they say no and you truly believe in the idea, leave and build it anyway. You can negotiate your building of this with a new employer upfront if needs be.