Among the banks that rule Wall Street, Citigroup got a bailout that was bigger than the rest. Now the company is about to pay a king’s ransom for its federal rescue. The Obama administration is making final preparations to sell its stake in the New York bank, according to industry and federal sources. At today’s prices, the sale would net more than $8 billion, by far the largest profit returned from any firm that accepted bailout funds, and the transaction would be the second-largest stock sale in history. On paper, the government’s 27 percent stake has grown in value to $33 billion. The size of the deal in the works has Wall Street buzzing. Only the stock offering by Japan’s Nippon Telegraph and Telephone, which raised $36.8 billion in 1987, was larger, according to Thomson Reuters. Leading financial firms, including J.P. Morgan Chase, Morgan Stanley and Goldman Sachs, are vying to be chosen as the deal’s underwriters to gain the prestige of managing a historic stock sale as well as the fees from investors who buy the shares. To improve their chances, some banks, such as Goldman Sachs, are offering their services to the Treasury Department at almost no cost, industry officials familiar with the matter said. The windfall expected from the stock sale would amount to a validation of the rescue plan adopted by government officials during the height of the financial panic, when the banking system neared the brink of collapse. A year ago, Citigroup’s stock hovered around a dollar a share, and the bank’s future seemed in doubt. On Friday, the stock closed at $4.31.