A verbal "go ahead" won't help you. If they wanted to litigate in the future, they would either way. Bringing it up to your employer would only impact your care

A verbal "go ahead" won't help you. If they wanted to litigate in the future, they would either way. Bringing it up to your employer would only impact your career prospects and not benefit you in any way. They would just treat you as potentially leaving, or disengaged and you will be less likely to earn promotions etc. Its best just to keep it to yourself. If you are worried, keep records of working on it on your own time, in case it becomes an issue. If your side project takes off, you tell your company you are leaving to do your own thing, and generally most companies don't care. It's only if they discover that you are doing something that directly competes, then they will look into it.