MEXICO CITY (AP) _ The son of one of Mexico's most revered 20th century leaders has agreed to seek the presidential nomination of a venerable minority party, an aide said Tuesday.

Cuauhtemoc Cardenas, son of the late President Lazaro Cardenas, was a leader of the so-called Democratic Current movement seeking reforms within the Institutional Revolutionary Party that has ruled Mexico since its founding in 1929.

His aide, Armando Machorro, said in a telephone interview that Cardenas agreed Monday to seek the nomination of the Authentic Party of the Mexican Revolution but was not expected to make any public statement until Wednesday.

Cardenas and Mexico's onetime ambassador to the United Nations, Porfirio Munoz Ledo, formed the Democratic Current last year demanding that the ruling party, known as the PRI, open up its presidential nomination procedure.

In Mexico, the president traditionally picks his successor for a six-year term. Carlos Salinas de Gortari, budget secretary in the administration of President Miguel de la Madrid, was named on Oct. 4 as the PRI's presidential candidate for next July's election.

The PRI leadership severely reprimanded the Democratic Current last spring, but its protests continued. The movement's membership is uncertain but it was known to have some sympathizers among influential Mexicans.

The current issued a statement Monday saying, ''It is indispensable to repudiate'' Salinas de Gortari's nomination and called for supporters ''to rescue the dignity of militancy and put loyalty to principles above servile obedience.''

The ruling party never has lost a presidential, senatorial or gubernatorial race and is Salinas de Gortari is certain to be elected. The PRI is synonymous with the government and controls the electoral process.

In an apparent gesture to calls for a more democratic procedure, the party announced six leading candidates - all Cabinet members - and held a public forum in which each separately expressed his political views.

The choice of Salinas de Gortari, however, then proceeded according to tradition.

Francisco Lupian, spokesman for the Authentic Party, known as the PARM, said it has yet to complete its plans for choosing a presidential nominee at a convention.

Machorro, however, said it was his understanding that the only other declared candidate, 45-year-old lawyer Adolfo Kunz Bolanos, would withdraw ''if Cardenas' candidacy is ratified by the assembly.''

Cardenas' most important elected post was governor of the central state of Michoacan.

The PARM was founded in 1954 and often has supported the ruling party's candidates in national elections. At times, it has been in danger of losing its formal registry, which requires obtaining 1.5 percent of the vote.

The elder Cardenas was president from 1934-40 and is regarded as a national hero for, among other things, the nationalization of the oil industry.