WASHINGTON — Christine Lagarde, the managing director of the International Monetary Fund, joked on Monday about donning “dream binoculars” and seeing the possibility of relocating the group’s headquarters to China.

“We might not be sitting in Washington D.C.,” Ms. Lagarde said at a Center for Global Development event here in which she envisioned what the I.M.F. might look like in 2027.

Ms. Lagarde may joke, but her comments reflect a concern that world leaders have about the changing role of the United States in global organizations. The articles of the organization say the headquarters should be the country of the member with the largest economy.

When the United States, Britain and other global powers met in Bretton Woods in 1944 near the end of World War II to stabilize the world’s economies, the United States’ overwhelming economic power was reflected in the decision to base both the I.M.F. and the World Bank in its capital. It is a decision that is sometimes questioned given the growth of economies like India and China.