Sure. Granting agencies fund research in the private sector all the time. I doubt you’d convince anyone to give you money as a private individual, but if you formed your own company or non-profit organization and established a track record of useful work in research and/or development, preferably in cooperation with universities or other companies doing funded research, then you could most definitely submit a proposal that would attract serious consideration and might end up getting funded.
I’ve worked on government-funded research projects where the principal investigator (i.e., the entity which conceived the project and in whose name the proposal was submitted) was, as far as I know, a sole proprietorship or partnership with no employees other than the owner(s). The projects were large enough that the work was divided among several public institutions and private companies, each of which had signed onto the proposal, and was paid separately by the granting agency.
So if your little sole proprietorship has a great idea for a research project, go talk to your friends in industry and academia about how you’re going to divide up the work and then submit your proposal. Just keep in mind that you probably won’t get all the money at once… you’ll get a little bit at a time, and will need to submit reports, provide other evidence of work and useful results, and comply with a bunch of other bureaucratic requirements to keep the cash coming.