Does Ebay let you do a "buy it now" that is closed to everyone except one specific bidder?

Is it possible to set up a "buy it now" on Ebay so that only one specific person who you have chosen beforehand can win the auction? I have a potential buyer who wants the sale to go through Ebay but he wants to be sure only he can win it.
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You're not supposed to but they probably won't find out.
<< <i>Or just cancel the auction and do it off ebay.
You're not supposed to but they probably won't find out. >>
The item is not currently on Ebay. However, the buyer wants to go through Ebay.
I was reading some eBay forums, and they said just do it as a fixed price listing, put in the description it is just for bidder xxxxxx just in case and as soon as you list it, e-mail him the # so he/she can get in and purchase it.
Edit: another person suggests:
List it as an auction rather than as a fixed-price listing. Use the agreed-upon price as the opening bid amount, start the listing and send the item number to the intended buyer. If the "wrong" person bids on it you can cancel their bid and when the intended person bids you can use the seller's right to end an auction at any time to sell to the current high bidder. This strategy eliminates the possibility that the "wrong" person will find and use a Buy It Now, and you don't have to worry about scheduling and timing.
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<< <i> List it as an auction rather than as a fixed-price listing. Use the agreed-upon price as the opening bid amount, start the listing and send the item number to the intended buyer. If the "wrong" person bids on it you can cancel their bid and when the intended person bids you can use the seller's right to end an auction at any time to sell to the current high bidder. This strategy eliminates the possibility that the "wrong" person will find and use a Buy It Now, and you don't have to worry about scheduling and timing. >>
This sounds like a very feasible idea - thanks to all for responding.
just list it for what they want the buy price to be with a BIN
send them the item number
if you list it in some obscure category, no one will find it
in the description - put what the guy wants, and then write this is an auction for (your buyer)
hopefully no one else hits the BIN, or if they do then you have 2
some buyers would rather go through eBay/PAYPAL because they have a little buyer protection
if you happen to have a store - depending on value, it may be cheaper to list it there
I've done it for a buyer who was standing by on the other end of the auction as I lowered the BIN. As soon as I lowered it he pressed the button.
Great transactions with oih82w8, JasonGaming, Moose1913.
<< <i>Have him list the item at a predetermined time and send you a link as soon as he lists it and then go for it. >>
I found a newly listed coin that was intended for someone else, Not realizing they had put some high shipping on the auction so others would not bid. Had I not wrote or they put normal shipping I would have bought that coin.When the seller explained I backed off. I just happened upon it before the buyer did. The buyer bought it 10 minutes later
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<< <i>How about doing an overly inflated price Buy it Now with the Best Offer option. Accept the agreed upon price from the buyer. >>
That's what I would do also.
If it's an expensive item that would cost you a lot to list as a BIN/BO and you don't know him or have any suspicions that he might not follow through, tell him the pre-condition is that he pay you your listing fees, eBay's end-of-auction fees and PayPal gimmees up front - BEFORE you list it. If he won't agree to that tell him sorry kiddo but no sale!
- Jim