Dude, I feel for you. The horse I was very attached to was almost mine and then she was sold out from under me. Luckily a working student bought her as a project pony, so she might be for sale at some point
I'm going to give you the same advice that was given to me: make a plan, don't look desperate, don't fall apart.
1.Start by looking for details. Is this horse going to be for sale soon? Is someone else interested? How much would she/he be selling for?
2.Have answers. If they ask questions like "who is your vet?" and "where would you keep them?", have answers prepared. Don't sound like you're reciting them, though.
3.Get the funding. Horses are expensive. Its a known fact. So known that they will be sure to know it.
4.Be at this horses level. Ah. Now this is where I ran into trouble with 'my' horse. She is a young TB and she needs training. And we're Eventers. Double whammy. If you and this horse are compatible in that way too, you're already one step closer.
5.Know the person. Are they compassionate about horses? If they are, be compassionate. If they are motivated by money, I don't like them, but money will go from talking to screaming in a matter of minutes.
6.Don't melt down. That won't help anyone, and it will give them a bad impression of you. Be cool, be calm, but not enough so you look detached. Just enough so you look professional.
7.Don't negotiate too much. Remember, if you act like a sleaze ball, they will treat you like a sleaze ball.
8.Have a Plan B. You have a Plan B. Don't freak out if Plan A doesn't go well, because you have a Plan B.
Stick to this and everything will be fine. This is not a sure plan, but its one of your best shots. Believe me, I know.