Peking has suddenly relaxed its emigration restrictions, bringing a significant jump in the numbers of Chinese residents moving to the United States and greatly improving China's chances of trade concessions from Washington.

U.S. consular officials here said today that certified Chinese immigration applications, which numbered only about 25 to 30 per month a year ago, would probably exceed 2,000 this month and gave no sign of slackening.

"I just don't know what the potential is," said a consulate official, who has requested more staff to handle the deluge. "There are a lot of people in China."

An official in the U.S. Liaison Office, which may begin to handle some of the applications after it becomes an embassy March 1, said China is allowing so many of its citizens to emigrate that they might soon reach the limits imposed by the U.S. government.

The sudden relaxation of Peking's restrictions on emigration to the United States, and to many other parts of the world, should significantly improve chances of winning most-favored-nation trading status for Chinese goods entering the United States. American businessmen and bankers say the trade benefit, which could cut tariffs on Chinese goods by as much as 200 percent, is necessary to give the Chinese enough cash to buy more American products.

The 1974 Jackson-Vanik amendment precludes trade benefits to Communist countries that unduly restrict their citizens' right to emigrate. But Rep. Charles A. Vanik (D-Ohio) and an aide to Sen. Henry M. Jackson (D-Wash.) said recently that Congress might be willing to grant China a waiver particularly if Peking relaxed its emigration restrictions

A U.S. consulate official here said applications from Chinese citizens who have been allowed to enter Hong Kong from China to apply for U.S. visas climbed steadily but slowly last year, then jumped to 500 in November and nearly 1,000 in December.

The emigrants have been granted exit permits by Peking after showing Chinese officials a U.S. government certificate sent to them by relatives in the United States that affirms they meet the requirements for a U.S. visa.

An official here said the consulate has been notified that certificates for 15,000 to 17,000 more Chinese resirents who have not yet arrived here have been cleared in Washington.

"We estimate 99 percent of those who leave China and apply here will go on to the United States. There is a very small fallout rate," the official said.

The change in Chinese policy appears to be at least as much a product of Peking's desire to win friends among overseas Chinese as it is to increase the chances of U.S. trade benefits. Liao Cheng-chih, the Central Committee member responsible for overseas Chinese affairs, announced a year ago that Peking hoped to ease restrictions on Chinese who wished to travel abroad.

There are 22 million people of Chinese ancestry who live outside China, many of whom have relatives on the mainland. There are 17 million Chinese on Taiwan who also would be targets of such a policy.

Sen. Edward M. Kennedy (D-Mass.) visited China at about the same time as the Liao announcement and gave Chinese officials 22 requests from U.S. residents seeking permission for relatives to leave China. Officials here said they did not know how many of those on Kennedy's list had since been allowed to leave, but that several had appeared at the U.S. consulate here.

Officials said they expected many more Chinese residents would be receiving certificates allowing them to leave as their relatives in the United States learned of the relaxation of restrictions. In a few cases, Chinese officials have become so Generous with exit permits that they have granted them to residents who presented photocopied foregeries of the necessary U.S. government certificate, known as I-171. The forgeries appear to be the work of relatives in the United States who want to claim a close family relationship to a distantly related person who would not otherwise qualify for a U.S. visa.

No more than 20,000 Chinese residents are allowed to emigrate to the United States each fiscal year under current U.S. law. In the past that quota has been filled mostly by long-time Hong Kong residents born in China, Taiwan residents or refugees who crossed the border illegally into Hong Kong. Spouses, parents or minor unmarried children of U.S. citizens are not included in the quota and some of the new Chinese emigrants are parents of Chinese-Americans.

Unless the U.S. law is changed, growing numbers of emigrants from the Chinese mainland could seriously slow the movement of Hong Kong and Taiwan residents who wish to emigrate to the United States.

The 2,000 Chinese emigrants who applied for visas this month will probably not leave for the United States for two or three months, since the consular staff has been used to handiling far fewer applications and has had to delay interviews and paperwork. About 300 emigrants, most of whom applied no later than October, are expected to leave this month for the United States.

The relaxed emigration restrictions have had a severe effect on Hong Kong, which only received 26,000 legal immigrants from China in 1977. In 1978 the figure nearly tripled to 71,000, with about half arriving in the last three months of the year.

Hong Kong emigration officials said most of the Chinese emigrants arriving here are staying in Hong Kong.

"The only countries that seem ready to take in refugees in any large numbers are the U.S. and Canada," one official said.

A few emigrants manage to join relatives in Britain, Australia, Mauritius, Venezuela and other countries with relatively large Chinese communities, but immigration quotas are generally strict. Many Chinese arrive here planning to go on to the Philippines, Indonesia and other Southeast Asian nations but find they cannot get visas.

A few of the emigrants applying at the consulate already have a claim to U.S. citizenship. One, Daniel Kelly, left for the United States yesterday after more than 20 years of trying to escape China. Kelly told United Press International that after his father, an American missionary, died, Chinese authorities refused to acknowledge his U.S. citizenship, apparently because his mother was Chinese.

Kelly said he served several years in prison and labor camps after trying to swim across the border to Macao in the late 1950s. Chinese authorities allowed him to leave China on Dec. 23, along with his mother, his wife and three children. The UPI story said they were bound for Plainfield, Ind., where they will live with Kelly's sister and her husband.