President Li Xiannian of the People's Republic of China arrived here yesterday on a state visit, just as President Reagan nominated Winston Lord, until recently the president of the Council on Foreign Relations, to be U.S. ambassador to China.

Li, 76, is to meet with Reagan at the White House this morning and with Cabinet officials this afternoon on a wide range of issues including the sale of nuclear-power technology, relations with Taiwan, problems with the Soviet Union and U.S. trade and population-control policies.

Officials said they were optimistic that a long-delayed nuclear trade pact might be among agreements to be signed today.

Reagan, who left the hospital Saturday, a week after intestinal surgery, is expected to abbreviate his ceremonial appearances but will not shorten any substantive talks with Li, White House officials said.

"If we can get a nuclear agreement, that's fine, but it's not the main purpose of the meeting," a senior administration official told reporters.

Lord, 47, resigned last month as head of the council, apparently in preparation for this nomination. He was a Foreign Service officer who became policy planning director at the State Department under then-Secretary Henry A. Kissinger, serving as Kissinger's main speech writer and a senior adviser. Lord took the council job, in effect the leadership of the U.S. foreign policy establishment, in 1977.

Lord is expected to win easy confirmation in the Senate to replace Arthur Hummel.

Lord's wife, Bette Bao Lord, was born in Shanghai of Chinese parents and came to the United States when she was 8. She has written two novels about prerevolutionary China, "Eighth Moon" and "Spring Moon."

Chinese leaders have made it clear that the status of Taiwan remains a major area of friction with the United States and one problem that will not be resolved during Li's visit, although it will be discussed. Relations with the Soviet Union, China's modernization effort and the mutually cautious plans to lower trade restrictions are expected to dominate the private talks.

Li, a former guerrilla leader and one of the last survivors of Mao Tse-tung's historic "Long March" in the mid-1930s whose participants became the revolutionary vanguard, has mainly ceremonial duties as head of state. One of the founders of the Communist Party in China, he has survived roller-coaster politics during 29 years on the Politburo and is one of six members of its ruling Standing Committee.

He is a veteran economic administrator and an important figure in formulating China's foreign policy.

Administration officials will also pay substantial attention to the No. 2 member of China's 14-person delegation, Vice Premier Li Peng, an engineer and computer expert who is considered a possible successor to Premier Zhao Ziyang. The vice premier is to visit California's Silicon Valley, Hoover Dam on the Nevada-Arizona border and other sites after the Chinese delegation opens a consulate in Chicago Thursday.

The United States did $6.5 billion in trade with China last year; a projected $6 billion in nuclear power-plant sales could be opened to U.S. bidding under the pending trade pact.

But Reagan has not yet approved the trade package's submission to Congress, where reaction to some provisions is expected to be mixed. The senior administration official said that China "has come a very long way in the last two years" in committing itself to block the spread of nuclear weapons and that the administration would provide written assurances to Congress that it is confident China will abide by those commitments.

"It is in China's own interests" to maintain safeguards, the official said, and "it is true that to a very considerable degree we rely on China's perception of its own interests" to guarantee its cooperation.