A possible regional and factional battle for control of the Democratic National Committee shaped up yesterday as two -- and perhaps three -- challengers began their drive to overhaul the front-runner for the job, Los Angeles attorney Charles T. Manatt.

As Manatt, the former California state chairman and current head of the party's national finance council, completed a two-day round of meetings with President Carter, Vice President Mondale and leading congressional and labor leaders, the first clear signs of opposition to his candidacy emerged from the Northeast and the Midwest.

New York national committeeman Patrick J. Cunningham and Missouri national committeeman Charles E. Curry launched their campaigns in letters to colleagues on the committee.

The name of Arkansas Gov. Bill Clinton, who was defeated for reelection in November, also bobbed back into speculation. Clinton had apparently backed away from running in pre-Christmas discussions, but several sources reported the governor had indicated during a visit to the White House Wednesday that he was taking another look at the race. Clinton was en route back to Little Rock yesterday afternoon and was unavailable for comment.

The Democratic National Committee is scheduled to meet in late February to choose a successor to retiring chairman John C. White, a former Texas agriculture commissioner who was picked for the job in 1978 by President Carter and is a victim of Carter's landslide defeat.

Efforts have been made by Mondale, Sen. Edward M. Kennedy (D-Mass.) and Speaker of the House Thomas P. (Tip) O'Neill Jr. (D-Mass.) to avoid making the choice of a new chairman the first round in the fight over the 1984 nomination. All have called for a party chairman who is neutral on the 1984 choice and experienced in fund-raising and organization.

Manatt, 44, who tried for the national chairmanship eight years ago and lost to Robert S. Strauss, has mounted the most aggressive campaign for the job and for weeks appeared to have no serious challenger. He is still regarded as the frontrunner by knowledgeable Democratic sources. But emergence of candidates with regional support in the Northeast, the Midwest and (if Clinton takes the plunge) the South could set the state for a more serious battle.

Cunningham, 52, the Bronx Democratic chairman for nine years and the New York Democratic chairman from 1974 to 1977, has been on the national party executive committee the last eight years and was instrumental in bringing the last two Democratic conventions to Madison Square Garden. He helped elect Hugh Carey as governor in 1974 but was forced out of the state chairmanship by Carey after his indictment on charges he had arranged a judicial nomination in return for a promised payoff. Cunningham was later cleared.

Curry, 62, while less well-known nationally than Cunningham, has been a member of the national committee since 1976 and is the head of its Midwest caucus. A wealthy businessman who recently divested himself of control of his savings and loan and investment companies, Curry has been a leader in reform efforts in Kansas City and served for eight years in a job Harry S. Truman once held -- presiding judge (chief administrator) of Jackson County. On the national level, he has organized business support for ratification of the Equal Rights Amendment and worked in the presidential campaigns of Sen. Henry M. Jackson (D-Wash.).

Clinton, 34, an upset victim in his bid for a second term as governor of Arkansas, is an early Carter supporter who also enjoys political backing of some of the party's leading liberal activists. He has hesitated about seeking the chairmanship because a four-year term would take him out of contention for elective office in Arkansas.

Manatt is a senior partner in a rapidly growing and politically influential Los Angeles law firm which opened a Washington office a year ago. A backer of California Gov. Edmund G. (Jerry) Brown Jr. in the 1976 Democratic presidential contest, Manatt switched allegiance to Carter in 1980. Last month, he helped Kennedy raise funds to retire his 1980 campaign debt. He has been more active than anyone in seeking support for the party chairmanship, lining up backing from key congressional figures and holding a series of dinners across the country to woo national committee members.