In order to keep eBay auctions legitimate and prevent sellers from bidding on their own auctions, there is no way to determine the maximum bid amount entered by the current high bidder. While you cannot see the current high bidder's maximum bid, you can view the maximum bids of previous bidders after they have been outbid by another buyer. Looking up previous maximum bids on eBay is a fairly simple process.
Open the item description page for the auction.
Click the link under the bidding section entitled "Bid history."
Review the list of previous bids. Here you will be shown a list of bidders, the date of their bid and the previous maximum bid amount.