President Reagan, who has already demonstrated his ability to be flesible in the face of changing political circumstances, is believed to be moving toward a reveersal of his longtime opposition to an extension of the Voting Rights Act of 1965 in its current form.

Much of the impetus for this change, which would put the administration on the side of civil rights and other liberal groups seeking to extend the act, is coming from political advisers who have concludd there is little to be gained and potentially much to be lost politically in the South by opposing an extension.

That political analysis was given added credence this month by the results of a special congressional election in Mississippi. Democrat Wayne Dowdy, initially given little chance against a well-financed Republican in the conservative district, campaigned hard for extension of the act, accused Reagan and the Republicans of planning to kill it, and rode a large turnout in the district's black precincts to a narrow victory.

The implications of the Dowdy victory have not been lost on the White House, according to an official who confirmed that the president's political advisers are likely to urge support for an extension of the act.

"A lot of people assumed that the politics in the South would cut in favor of non-extension," he said. But noting the outcome of the Mississippi special election, this official said that extension is of Great importance, substantively and symbolically, to blacks," and may be an issue around which the Democrats could organize an effective opposition to the administration.

Reagan is not expected to make a decision on the Voting Rights Act until after a review of the law's provisions, scheduled for completion by Oct. 1, by Attorney General William French Smith and lawyers at the Justice Department. But the president's general direction was indicated, the White House official said, by the fact that he has already backed off his longtime belief that, if the act is extended, it should be applied to the whole country and not to selected targets guilty of discrimination in the past.

At a recent meeting with black state legislators, Reagan was quoted as saying he was having second thoughts about applying the law nationwide. That was good news to black leaders, who argue that such a change would weaken its enforcement in the areas where voting rights violations remain a problem.

Enacted in 1965 and extended in 1970 and 1975, the law will expire in August, 1982, unless extended again. It currently applies to six southern states and parts of 16 other states, requiring them to get Justice Department approval for any changes in their election laws.

This week a House subcommittee approved a 10-year extension of the law with no significant changes. But efforts to weaken it are expected in the full Judiciary Committee and on the House floor. Moreover, the measure must also clear the Senate, where it faces even stronger opposition.

On the surface, the measure is the antithesis of the Reagan political philosophy. The president is committed to returning a maximum of power and responsibility to the states, while the Voting Rights Acts places the ultimate authority over election laws in the hands of the federal government in a number of states. Some of Reagan's earliest and strongest supporters are conservative white southerners who have long objected to the application of the law to their states.

But the president has also proven himself to be flexible in his philosophical tenets when they collide with the necessities of practical politics. And in the case of the Voting Rights Act, the practical political course may be to avoid a fight by supporting extension of the act as written.

This, at least, is the kind of advice being given to the White House by such people as Harry Dent, a longtime Republican political operative in the South. Dent said in a recent interview that he relayed his views on the issue to David Gergen, a senior White House official.

"The whole question is kind of passe in the South," Dent said." "But the question of voting rights is not passe for black people."

Dent said that most white southerners have "learned to live with it," meaning there is not much to be gained among them by an attempt to kill the act or seriously weaken it. But blacks do care deeply about the law, which in 15 years has greatly enhanced their political power throughout the South, he said.

"The Mississippi vote was an indiciator of what can happen," Dent said. "This is the one issue that can unite and spark a turnout. It is a call to political arms for blacks."