National Hispanic leaders, presenting a strong political challenge to the Carter administration, have launched an intensive lobbying effort to have a Mexican-American appointed as the next ambassador to Mexico.

Apparently in a late effort to influence the choice of a successor to Ambassador Patrick J Lucey, whose recall is considered imminent, the leaders have presented the Carter administration with a list of alternative candidates to the odds-on favorite, former congressman Bob Krueger, a Texas Democrat who was defeated in his attempt last year to oust Republican Sen. John G. Tower.

But Krueger has some powerful backers in the White house, among them special trade representative Robert S. Strauss and Hamiltton Jordan President Carter's chief political adviser.

Lucey, a former governor of Wisconsin is expected to return to Washington Shortly to take over a new State Department task force that will coordinate U.S. policy toward Mexico. He is being pushed for that job in the State deaprtment by those who believe the task of dealing with the several government agencies that affect policy toward Mexico would be best handled by a political figgure with independent standing rather than a career official.

Lucey, however, is wanted back in Washington by White House political advisers for another reason - to be close at hand for advice and assistance during the 1980 presidential campaign. Today, for example, Lucey is scheduled to accompany Carter on a one-day political trip to the ambassador's home state of Wisconsin, an often pivotal presidential primary testing ground.

The lobbying effort over the ambassadorial appointment comes at a time of sensitive dealings between the United States and Mexico over oil, trade and immigration policies and growing dissatisfaction between the Carter administration and Mexican Americans who voted overwhelmingly for Carter in 1976.

Moreover, it is a sign of the increasing attemp by Hispanics to exert their political muscle at a time when they are the nation's fastest-growing minority and who in the 1980s will replace blacks as the United States' largest minority group.,tAmong many Hispanics, the choice of a successor to Lucey is seen as a political litmus test of the Carter administration's promise to appoint more Hispanic-Americans to important federal positions.

They see the choice of a successor to Lucey as an opportunity for Carter to name a Mexican-American to an important post at an important time in U.S. dealings with Mexico.

While the Carter administration has made no announcement on Lucey's fate, The Washington Post has learned that Mexico is on the agenda for today's meeting of the ambassadorial appointments review commission, at which it is expected that Abelardo (Lalo) Valdez, an assistant administrator of the Agency for International Development, and perhaps four other Hispanics will be discussed as potential ambassadors to mexcio.

Other suggestions from the Hispanic community are Esteban Torres, the 49-year-old U.S. representative to the United Nations Economic, Social and Cultural Organization in Paris; former New Mexico governor Jerry Apodaca, who is chairman of the president's council on Physical Fitness; and Cristobal Alderete, chairman of the Southwest Border Regional Commission.

Also being floated by Hispanic Groups are the names of former Arizona governor Raul Castro, now ambassador to Argentina, as well as Graciela Oliverez, director of the U.S. Community Services Administration.

National Hispanic leaders stressed that their lobbing efforts with the White House now are not so much against Krueger or in behalf of any individual Mexican-american. Rather, they say, their main goal is to see that a Mexican-american is appointed to the post, and the names being suggested are designed to show that qualified Hispanics are available for the post.

However, an administration official, noting that the United States has seven Hispanic ambassadors, said that the administration does not consider it necessary to have a Hispanic assigned to Mexico City and that Carter generally "has not done the ethnic bit" in appointing ambassadors. For example, the official said, it has not been traditional for the United States to have "an active Jewish American" as ambassador to Israel.

Hispanic groups also pushed for the appointment of a Mexican-American to Mexico City at the beginning of the administration. But in the end a political figure, Lucey, won out.