What discount they'd agree to (if any) will depend on a lot of factors.
From my discussions with other landlords and reading on landlord discussion boards, many don't want to deal with prepayment. The primary concerns seemed centered around potential for it to be ill-gotten cash or just feeling like anything outside the normal monthly payment was just weird/unnecessary. Some, like me, don't feel the need to discount because we have very low non-payment rates.
I've been offered a half year's rent in advance and turned it down because they had no documented income source/credit history. Even if it had been an otherwise well-qualified tenant who pitched the idea of a full year up front I'm not sure I'd give much discount for it. It does eliminate non-payment risk, but it would throw off my income for that first year and the year I switched back to monthly, not everyone would care about that, but I doubt I'm the only one.
As a tenant, paying for a year up front carries risks. There are times when a tenant is justified to withhold rent, if you've already paid it you've given up that leverage and a crappy landlord could take advantage (imagine a broken furnace/water heater for months). If they are in a bad spot financially they could take your year of rent, stop paying the mortgage, and bail on the rental altogether, which would be at minimum an annoyance to you and potentially quite costly.
In my market, I have no interest in discounting rent. I think that in general, at most, a 5% discount is reasonable for those interested in entertaining the notion at all. If it's an area where eviction rates are quite high they have already baked a high non-payment rate into their rental rate, so they will have more room to negotiate on guaranteed payment and I bet 10% would be pretty agreeable in such markets.
It doesn't hurt to ask, but I'm not convinced it's worth the risk to you.
I'm in the US, depending on country some of the considerations above might not apply. In the US landlord/tenant rights vary by state, so the withholding rent statement might not apply where you are.