While one arm of the Reagan administration is trying to sell the government-owned Conrail system to the highest bidder, another agency is giving away a government-chartered corporation worth at least $1 billion.

The government could earn more than $2 billion from the sale of Conrail, but it does not stand to make a dime on a deal cooked up by the Federal Home Loan Bank Board to dispose of the Federal Home Loan Mortgage Corp.

Commonly known as Freddie Mac, the Mortgage Corporation -- as it prefers to be called -- is a congressionally chartered profit-making business that raises funds for home mortgages. Freddie Mac has financed more than $90 billion of mortgages since it was founded in 1970.

With assets of more than $8.9 billion, a capital base of $1.25 billion and 750 employes, Freddie Mac is the third-largest financial institution in Washington. Though a private corporation, Freddie Mac is run by the three presidentially appointed members of the Federal Home Loan Bank Board.

Some White House officials have proposed "privatizing" Freddie Mac as part of their effort to get the government out of private business, but Bank Board Chairman Edwin J. Gray has decided to give it away instead.

The billion dollar gift from Uncle Sam will be bestowed on the nation's federally chartered savings and loan associations, which by any definition qualify as among the truly needy.

Sometime after Christmas, the savings and loans will be given $600 million worth of preferred stock in Freddie Mac. The stock does not give them total ownership of Freddie Mac, but preferred stockholders will be entitled to the first $10 million in dividends Freddie pays plus 90 percent of any additional dividends. Strictly speaking, they're not giving away the store, they're just giving away its profits.

No one can argue that the S&L's don't need help. After years of mismanagement, compounded by misguided deregulation, most savings and loans are slowly going broke. Little by little their net worth is being eaten away by high interest rates and bad loans, forcing federal regulators to resort to creative accounting and under-the-table bailouts to keep them alive.

The net worth of savings associations has dropped so steadily in recent years that federal regulators have again and again lowered the minimum standards of fiscal health. And when dropping the passing grade did not keep the associations from failing, the regulators gave them artificial assets to make their scores look better.

Gray readily admits the Freddie Mac giveaway is yet another ploy to make the S&L industry look healthy. The Bank Board calls the deal a "paper transfer that does not change in any way the direction, operations or statutory purposes of Freddie Mac."

That's one of the things wrong with the deal, critics of Gray's generosity complain. They think Freddie Mac ought to change, that the government ought to get out of the mortgage business, in the same way it is getting out of the railroad business by selling Conrail. Like its cross-town counterpart Fannie Mae -- the Federal National Mortgage Association -- Freddie Mac could easily sell stock to the public and free itself from the government.

The giveaway dreamed up by Gray will lead to trading of Freddie's preferred shares on the New York Stock Exchange, but only savings and loan associations will be able to buy them.

The transaction is as complex as the financing techniques Freddie Mac uses to raise mortgage money: The 12 regional home loan banks, which put up $100 million to start Freddie a decade ago, now own all its stock. In January, Freddie will give the 12 regional banks a special stock dividend of new preferred shares; the regional banks will then distribute the preferred shares to individual savings associations in proportion to their ownership of the regional bank.

Until the unexpected and undebated decision to give away the preferred stock, Freddie Mac was carefully being eased out of Uncle Sam's nest. As of next year, Freddie for the first time will have to pay taxes on its profits, an important step away from being a ward of the state.

But continuing to wean Freddie will be more difficult now that Gray has decided to give away its preferred stock. So long as the preferred shareholders are entitled to more than 90 percent of Freddie's dividends, it will be hard to find much incentive for other investors to buy in.

If Freddie Mac went private, it probably would be run by a mixed board of directors much like that of Fannie Mae, whose board includes public members appointed by the president and private directors elected by the stockholders.

Instead, Freddie will continue to be run by the political appointees of the Bank Board, a situation of some concern to private mortgage bankers who sell mortgages to Freddie. They fear Freddie will be managed not to make money for itself or to maximize mortgage finances, but to benefit the struggling savings and loans. They fear that to strengthen the S&Ls, Freddie might pay out huge dividends that could weaken its own finances.

If the Bank Board is willing to give away Freddie's stock to prop up the savings associations, it obviously could make other politically motivated decisions to benefit holders of the free shares.

The potential conflict between the interests of Freddie's shareholders and the housing industry it is supposed to serve could be avoided if the Reagan administration would stick to the principal of privatization. Getting the government out of quasi-governmental agencies is what the President says he believes in and what he ought to do. If private ownership is right for Fannie Mae, Comsat and Conrail, it's probably fine for Freddie Mac.