Treasury Secretary-designate Donald Regan yesterday predicted that the prime interest rate, now at a record 21 percent, will soar very quickly to at least 22 or 22.5 percent before turning down to a "first . . . stopping place" of 16 to 17 percent sometime next year.

"We still have further to go," Regan said. He noted that Citibank in New York is paying 21 percent to borrow funds. "If they're paying 21 percent, right there you have a prime [interest rate] of 22 or 22.5 percent," Regan said. He added that "the longer the situation persists, the worse it will become."

But in a conversation with a group of reporters, Regan threw cold water on the idea that President-elect Ronald Reagan should declare a national economic emergency as soon as he takes the oath of office on Jan. 20, although he conceded that "we have a serious economic situation," and that the nation "is looking to Reagan to do something about it."

Regan refused direct comment on the troubled Chrysler Corp. (on which he had his first briefing yesterday from Treasury Secretary G. William Miller). But speaking in general terms, Regan said that "if we're going to have a competitive economy, we've got to recognize that there will be casualties. Everything can't be a winner."

He also indicated a strong position against curtailing imports as a way of helping the battered U.S. auto industry: Unless actual "dumping" of products can be shown, Regan said, "competition must come from without as well as from within in a truly competitive economy."

Just the day before, Regan's incoming chief of Staff, James A. Baker III, said that Reagan was considering declaring a national economic emergency, drawing on recommendations made by Rep. Jack Kemp (R-N.Y.) and by Rep. David Stockman (R-Mich.), Reagan's selection to be director of the Office of Management and Budget. Press reports on Baker's comments helped the stock and bond markets to rally.

Stockman and Kemp recommended that Reagan declare the emergency and demand that Congress devote its exclusive time for the first 100 days of the next session to solving the nation's economic, budgetary and regulatory problems.

But Regan said that "my rhetoric is something less that a national emergency." He said that all of the Stockman-Kemp ideas are valid, "but they were using a worst-case basis. That's where the confusion arises. I don't think we're there [at the worst case] yet."

Reagan's economic package -- which Regan stressed is not yet fully developed -- is based on four "legs": first, reduced spending; second, a strict monetary policy; third, an accent on productivity, and fourth greater savings stimulated by a large tax cut.

Regan said that President Reagan himself should be "the No. 1 spokesman" on economic issues. When he discussed his appointment to the treasury job with the president-elect, Reagan said, he hadn't asked that he be designated the principal spokesman on economic issues, although "that is the traditional role" of the treasury secretary.

"I don't have an ego problem," Regan laughted. "There are plenty of bright guys around" in the administration. It was at that point that he suggested that the president ought to be top spokesman.

Regan made clear that getting interest rates down will be a top priority of the Reagan administration, especially because today's record levels make it "precarious" for small businessmen to stay live. The present high rates have already crowded some borrowers out of the market, he said.

Asked how the administration would proceed to bring interest rates down, Regan responded: "I wish I were Mandrake [the magician].It won't come easy." But he added that if it is perceived that Reagan has an economic program that can be put in place quickly, there will be a change in both consumer and business psychology.

"Interest rates will come down almost as quickly as they went up. But they won't go back al the way," said the head of Merrill Lynch Co. He wouldn't say how low interest rates might eventually get, but projected 16 to 17 percent "as the first logical stopping place."

Regan said he wasn't yet prepared to comment on international economic issues, but noted that the dollar -- recently strong because of high interest rates -- "might fall as interest rates fall."