Republican Party leaders are so certain that Ronald Reagan will seek a second term that they have begun fighting among themselves over who will run his reelection campaign in their states.

"Everyone wants a piece of the pie," White House political director Edward J. Rollins said in an interview today. "Unlike 1976 and 1980, when only a few brave and courageous souls were willing to join with Ronald Reagan, everyone wants to be on the team."

This, he said as the Republican National Committee ended a four-day meeting here, has put the White House in a delicate situation in several states critical to Reagan's reelection chances. The question in each state is the same: how to blend longtime Reagan supporters and elected Republican officials into the same campaign.

In Illinois, for example, state GOP chairman Don Adams and Gov. James R. Thompson have told Rollins that they want to head a Reagan-Percy Reelection Committee to work for the president and Sen. Charles H. Percy (R-Ill.). Yet both have long been at odds with Don Totten, Reagan's chief political operative in the state.

In New Jersey, Labor Secretary Raymond J. Donovan ran Reagan's 1980 campaign and wants his political allies to play a major role again, Rollins said. Yet the state has a new Republican governor, Thomas Kean, who also wants a role.

GOP leaders, gathered at the site of the party's 1984 convention for their annual summer meeting, were told privately that the Reagan reelection effort will be run separately and be formally headed by Sen. Paul Laxalt (R-Nev.), the party's general chairman, according to several sources.

Reagan, they were told, may delay announcing his decision to seek reelection until after Thanksgiving, but a Reagan exploratory committee will be established in September. Republican National Committee Chairman Frank Fahrenkopf said Rollins will head "day-to-day operations" of the effort until a campaign manager is named, probably early in 1984.

Leading candidates for that job, he indicated, are William E. Timmons, a Washington lobbyist, and former transportation secretary Drew Lewis, now chief executive officer of Warner Amex.

Meanwhile, the general outlines of a Reagan reelection strategy are emerging. One interesting aspect is a calculation that the South will be severely split, partly because of Democratic registration gains among blacks, and that the region will provide the victory margin for whoever hopes to win the presidency in 1984, sources said.

This means that Reagan would have to carry several large, economically stricken midwestern and northeastern states such as Ohio, Illinois and Pennsylvania, as well as most of the West.

GOP leaders gathered here were extremely confident that Reagan will seek reelection and win. This feeling was in marked contrast to the group's last meeting in January, when there was gloom about the economy and an uneasiness about whether Reagan would run.

Party officials attributed the shift to the economic recovery and the president's improved standing in public opinion polls.

Rollins sensed so much optimism at the meeting that he went out of his way in a speech to caution party elders that they are in for a rough year in 1984 and that Reagan's reelection "will not be an easy task."

With a Republican governor and a growing party membership, things never looked better for the Texas GOP than they did a year ago when Reagan picked Dallas for the convention. But Gov. Bill Clements was defeated by Democrat Mark White last November and, in a speech three weeks ago, said it was "highly doubtful" that Reagan could carry Texas.