Step back a few steps.
Don't come with the product semi-developed. That gives you a poor position to negotiate and it, as mentioned in comments, might set off some red flags.
First things first, locate the person that has actual authority to invest in this. How far up the chain is he from your boss? Take a look at your company strategy. If your suggestion is breaking off from the company strategy (if it says to consolidate portfolio or whatever is business lingo for no new products, then scrap the idea - or be prepared to take your fight all the way up to the CotB)
Take some private time, write a report or something like it on what the characteristics of the product you want to develop are and what it's business possibilities are (b2b, b2c, eventual service agreements, exposure to new or old markets, etc) Don't overdo it, but mention these things - find out where the money is potentially coming from and roughly how much are we talking about. With this short report, ask for a short meeting with your boss. Ask him for permission to go see whomever has the authority to launch something, because you have an idea. Maybe the boss can help you with leverage. Once you have the ear of whomever is in authority, say something to the tune of...
Hey boss, I have been thinking about an opportunity I have spotted. I
have an idea for a new product. It will target ...(these existing
customers) and possibly be relevant for ...(customers in existing
market) or possibly even ...(customers in new markets). What I want to
do is ....(short description). I'd like the opportunity to develop
this further. What I need is to discuss it with one of our market guys
and then about (rough time estimate for alpha version) of my own time.
(Mention other resource needs). I strongly believe this can make money
for our shareholders. What do you think? In either case, I'll send you
a report of the things I have said now, I'll make it on my own time,
Then send him the report by mail. When and if this starts getting traction, is the perfect time to negotiate. But be aware that unless you have some god given skills you'll be hard pressed to gain any ownership of anything - but you can - if you show that you know how to - be put in charge of developing and implementing. You have already shown initiative. Initiative and know-how - The companys perception of these properties in a person usually end up being career- and salary changing for that person.
- Should I be trying to offer them a percentage to have a chance at
owning it? - NO
- Should I potentially ask for funding to get it off the ground? - YES
- Should I be feeling confident to be given ownership of the Intellectual
Property? - NO
You should not view this as your chance for ownership, you should view this as a chance to shine. Get it off the ground, get customers satisfied and you have a kick ass CV item and an extremely good position for next years salary discussion, or even bonus on completion, or possibly a significant bump up the ladder. Or all of the above.
If your target is ownership then you need to start your own company, develop it 100% on your own time, and only then offer it to the company with the leverage of quitting and selling it yourself. This will likely lead to severe legal issues, that you may or may not prevail through depending on how secure you can argue that you did not use company resources or client portfolios.