TOKYO (AP) _ The governing Liberal Democratic Party today began the process of selecting a successor to Prime Minister Yasuhiro Nakasone, with three candidates submitting bids to become Japan's next premier.

Finance Minister Kiichi Miyazawa and the party's secretary general, Noboru Takeshita, and its executive council chairman, Shintaro Abe, filed their candidacies for the presidency of the party this morning.

Due to the party's huge majority in the Parliament, the new party president is almost certain to become the next prime minister.

The three candidates said later that they hoped to reach a compromise agreement on Nakasone's successor in negotiations before Oct. 20. A possibility remained, however, that the new party leader could be chosen in a vote by the party's 445 Parliament members on Oct. 20.

''I believe it is best to develop a consensus inside the party as soon as possible,'' Miyazawa said. Abe and Takeshita echoed his statement.

Nakasone's term expires Oct. 30. The candidate selected to succeed him will be formally appointed at a party convention Oct. 31.

Nakasone has not yet committed his faction to any of the candidates. All three candidates today reiterated their pledges to continue his policies of transforming the economy into one less dependent on exports, and of maintaining a close security relationship with the United States.

A fourth contender for the post, former Liberal Democratic Party Vice President Susumu Nikaido, pulled out of the race Wednesday, saying he could not get 50 party Parliament members to support him, as required by party election rules.

Takeshita, 63, heads the largest party faction, with 114 members of Parliament. Miyazawa is second with 89 faction members, while Nakasone's group has 87 members. Abe's faction in the giant party has 86 members and former State Minister Toshio Komoto's has 31.

Takeshita is considered a patient and cautious negotiator, in contrast to the free-wheeling Nakasone, who won admiration abroad but occasionally irritated politicians at home. Takeshita has pledged to cut Japan's huge trade surplus, but has generally stressed domestic policies such as tax reform in his platform.

Abe, who was foreign minister from 1982 to 1986, has stressed improved relations with the United States. In a recent opinion poll, the 63-year-old politician fared well in ''international'' qualities but got lower marks in economics.

Miyazawa, 68, has served in most key Cabinet posts and enjoys a reputation as an expert policymaker with a good grasp of economics. But his campaign may suffer due to his distaste for party wheeling and dealing.

A recent poll by Kyodo News Service showed more than two-thirds of the presidents of 50 major corporations favored Miyazawa as the next prime minister, but about 80 percent said they expected Takeshita to win.

Nakasone's decision to leave office means the end of a five-year tenure that transformed Japanese politics, bringing a more visible, dramatic style to a nation long known for faceless politicians.

The new prime minister will have before him a full agenda of tax and administrative reforms initiated but not completed during Nakasone's years in office.