The Reagan administration, in a move that may precipitate a showdown with the People's Republic of China, will soon submit to Congress a long-delayed $97 million arms sale to Taiwan. Plans for the submission, made known to key lawmakers in recent days, came amid a continuing deadlock in the 2 1/2-month-old negotiations between Washington and Peking about arms sales to Taiwan.

China has threatened to downgrade its diplomatic and political relations with the United States across a broad front, including withdrawing ambassadors from the two capitals, unless a satisfactory solution is found to the dispute.

The sale of spare parts to Taiwan, announced by the State Department last Dec. 28, drew vehement objections from Peking. But further action was set aside during the negotiations, which began in mid-January.

U.S. specialists on China said the decision to move ahead is likely to make an agreement with Peking more difficult and might even cause the Chinese to break off the talks and take the anti-U.S. actions it has threatened.

The administration, in deference to Taiwan and its supporters here, earlier set an informal deadline of the end of March for submitting the arms package to Congress. According to one account, the administration plans to send the sale to Capitol Hill before the congressional recess begins April 9.

A senior State Department official yesterday refused to confirm or deny the reported decision to move ahead. The official said the discussions with Peking are continuing and that efforts, which he would not specify, are being made to resolve the issue.

Recent private and public signals from Peking, including statements attributed to Deng Xiaoping, the country's most powerful figure, have set forth a hardening Chinese position. From this and other evidence, U.S. officials increasingly think that the Taiwan arms issue has become part of an internal power struggle touched off by Deng's drive for sweeping administrative reforms and a purge of the Chinese bureaucracy.

Last Thursday, Deng was quoted in unofficial press reports as telling former Cambodian chief of state Prince Norodom Sihanouk, "We cannot accept the U.S. way of handling the Taiwan issue. We have no room for maneuver on this question. If things really cannot go on like this, then relations should retrogress. What is so terrible about that? I think the Chinese nation will continue to exist." According to the same accounts, Deng added, "We are now waiting to see; we are prepared for all eventualities."

On Friday U.S. industrialist Armand Hammer, after a meeting with Deng, quoted him as saying there can be "no compromise" on the Taiwan issue. Hammer, who signed a contract the day before for development of a vast Chinese coal-mining venture, suggested that a downgrading of political relations might not affect economic relations between the two nations.

There is considerable doubt in Washington that a deterioration could be limited to specific areas. U.S. diplomats have told their Chinese counterparts, according to an informed source, that potential reprisals could increase pro-Taiwan sentiment in the Reagan administration and among the American people, leading to a spiral of U.S. gestures and actions favorable to Taiwan, which in turn could bring a deepening U.S. crisis with Peking.

The global stakes in all this involve the Chinese weight in the international strategic balance between the United States and the Soviet Union.

Soviet President Leonid Brezhnev, in a bid to repair Sino-Soviet relations, called on China last Wednesday to set aside two decades of hostility and join in positive steps toward reconciliation.

Chinese statements issued Friday, however, seemed to spurn Brezhnev's olive branch.