In an e-mail to constituents on Monday, Harman said she filed paperwork notifying House officials that she was in discussions to succeed former Rep. Lee Hamilton, D-Ind., as the head of the center.
"I send this note because a decision is imminent and I wanted you to hear the news from me first," Harman wrote. "This is an excruciating decision because the distinction of representing the smartest constituents on earth will never be surpassed - nor will my relationships with my exceptional staff and colleagues in Congress. But shaping and leading the Wilson Center is a thrilling new challenge."
Hamilton stepped down from the position at the end of November, and the center's board of trustees is expected to choose a successor on Tuesday. The center is an organization designed to bring leading experts on various issues to Washington to interact with policymakers.
The 65-year-old Harman told constituents that "should this opportunity come to pass, I would be required to resign my seat." She said she would remain in Congress for several weeks to ensure an orderly transition.
Harman represents a Democratic-safe district that includes several beach front communities in suburban Los Angeles such as Venice and Redondo Beach. She was first elected to the House is 1992. After losing a race for governor, she regained the seat in 2000.
Potential candidates moved quickly to succeed Harman. Los Angeles City Councilwoman Janice Hahn announced her candidacy and California Secretary of State Debra Bowen said via Twitter she was giving serious thought to running for the seat. Hahn is the sister of former Los Angeles mayor James Hahn.
The secretary of state's office in California said once Harman resigns, Gov. Jerry Brown would have 14 days to call a special election. The contest is likely to be held in June. Primary elections would be held about two months earlier.
She is also one of the wealthiest members of Congress. Her husband Sidney Harman, is the founder of Harman International Industries and the owner of Newsweek.
Harman was one of the few California incumbents to face a credible primary challenge last year. She ended up defeating Marcy Winograd for the second time, winning about 59 percent of the vote.
Harman is a leading voice for Democrats on intelligence and homeland security issues. She was the ranking Democrat on the House Intelligence Committee when Democrats won control of the House in 2006, but fellow Californian Nancy Pelosi bypassed her and chose Rep. Silvestre Reyes to serve as the committee's chairman.
She is a member of the "Blue Dog caucus," a group of moderate and conservative Democrats whose ranks were greatly thinned in the November elections.
"I have always believed that the best solutions to tough problems require a bipartisan approach and bipartisanship is the center's brand," she told constituents, adding that the position would give her a unique opportunity to involve political leaders and experts in debates over the most pressing foreign and domestic policy issues.