The friend said a final decision is expected from the center's board of directors Tuesday, Politico reported.
The center, now led by Lee H. Hamilton, was established by Congress and is part of the Smithsonian Institution.
"It's not that she wants to leave Congress. It's more about seeing the Woodrow Wilson Center as the pre-eminent place for seeking bipartisan solutions," the friend, whose name wasn't disclosed, told Politico. "It's a classy, well-funded operation. She just sees it as a great challenge and a great opportunity. She kept getting more and more excited about it."
Harman, elected in 1992, is the ranking Democrat on the Homeland Security Committee's intelligence subcommittee.
Celebrity Families of 2014 [PHOTOS]