United Auto Workers President Douglas Fraser yesteday said the Chrysler Corp. will fail next year unless the incoming Reagan administration agrees to emergency measures to revive automobile sales nationwide.

Fraser and other UAW leaders sent a telegram to President-elect Ronald Reagan yesterday asking him to convene a "summit conference" on the American auto industry immediately after taking office to consider federal rebates for purchasers of new American-built cars and other special assistance.

The cost reductions proposed by Chrysler last week, including a 21-month freeze on the wages of Chrysler's UAW employes, are not enough to save the company if high interest rates and the current slump in auto sales continue, said Fraser, a member of Chrysler's board of directors.

"We are not facing a cyclical downturn from which there will be an inevitable and automatic recovery," Fraser and other UAW officials said in the telegram to Reagan. "Our nation faces the literal collapse of one of its most crucial industries if we stand idly by and allow the current conditions to continue in the months ahead."

Although Chrysler is hoping for rapid approval of its plan by the UAW in order to qualify for $400 million in federal loan guarantees, statements by Fraser and Treasury Secretary G. William Miller over the weekend made it clear that arrangements for more federal aid cannot be completed before Reagan takes office Jan. 20.

Fraser said again yesterday that he believes the UAW's contract with Chrysler should be opened for renegotiation, but he did not endorse the wage freeze proposed last week by Chrysler Chairman Lee A. Iacocca. "We can't solve the auto industry's problems today over the bargaining table," the union leader said.

The industry has been heading toward a crisis condition since Election Day, as rising interest rates cut short the fall recovery in sales. It now appears inevitable that the crisis will ripen just as Reagan assumes the presidency. If so, Reagan is likely to face a choice of either letting Chrysler slip into bankruptcy or making major revisions in his economic policies to help the auto sector -- the car manufacturers, suppliers, tire companies and dealers who are threatened by deteriorating car sales. A substantial policy tilt toward the auto industry could undercut the Reagan's commitment to cut government spending, a vital feature of his anti-inflation strategy.

Fraser said he and other UAW officials are not planning to meet with Miller until Jan. 6 -- the day after Miller returns from a vacation in the Bahamas. The union leader said he doesn't believe there will be any renegotiations with Chrysler on the wage freeze issue until after the meeting with Miller.

That in turn indicates that the government's Chrysler Loan Board, which Miller heads, will not be able to pass judgment on Chrysler's request for more loan guarantees until mid-January.Once the loan board approves new guarantees, Congress has 15 days to review the decision before Chrysler can actually issue notes and receive the cash.

Fraser said he agrees with Iacocca that Chrysler can survive until February or March without a new cash infusion, but not much longer.

The concessions Chrysler wants from the UAW, its suppliers and lenders -- estimated to total between $1 billion and $2 billion -- won't get the company through 1981 unless sales improve significantly, Fraser said.

For more than a month, sales have been at an annual rate of less than 7 million units, while Chrysler's recovery plans depend on a nationwide annual auto sales level of 8.8 million units in 1980 and 11 million units in 1981.

Auto industry experts are divided on whether auto sales can climb above the 10 million mark next year, and some fear that the combination of high auto sticker prices, high interest rates and a sluggish economy next year will continue to undercut consumer demand for new cars well into the future.

Fraser and the other UAW officials asked Reagan to assemble leaders of the auto industry, Congress and the new administration to consider the industry's plight.

The union made three proposals:

A special, congressionally approved tax credit that would give a cash rebate to each motorist who traded a used car for a new auto made in North America.

A government program giving federal payments to motorists who turn in older cars for scrap, further boosting the new-car market.

A requirement that companies selling a large volume of cars in North America be required to produce a significant percentage of their product where their market is -- in North America. This is aimed at forcing the Japanese auto companies in particular to establish parts manufacturing and assembly plants here.

In an interview Friday with reporters, Miller continued to defend the government's aid plan for Chrysler as being in the best interests of the taxpayer and the overall U. S. economy, as well as the company's interests.

He said Chrysler is exploring possible mergers and joint ventures with other auto manufacturers and will need such outside assistance to survive in the long run.

Chrysler has been discussing such ventures with Volkswagen, Mitsubishi Motors Corp. of Japan and Peugot-Citroen of France.

Miller said he didn't believe a joint venture is imminent in Chrysler's case. Certainly it won't occur unless the company is making a profit, he said.