The White House has interviewed two economists who served in senior positions in the George W. Bush administration to serve as the vice chairman of the Federal Reserve Board, according to people familiar with the matter.

The two are Richard Clarida, a managing director at money manager Pimco who is also a professor of economics and international affairs at Columbia University, and Lawrence Lindsey, who runs an economic-advisory firm in Washington.

Mr. Clarida served as assistant secretary for economic policy at the Treasury Department from 2002 to 2003. Mr. Lindsey was a top economic adviser to Mr. Bush from 2001 to 2002 and served as a governor on the Fed’s board from 1991 to 1997. Both men would satisfy the Trump administration’s desire to fill the vice-chair post with an economist with a strong grounding in monetary policy.

The Trump administration is also considering Mohamed El-Erian, the former chief executive of Pimco and a former deputy director of the International Monetary Fund.

It isn’t clear whether there are other candidates, or when a final nominee may be named. The process of selecting the central bank’s No. 2 official began in earnest last month after President Donald Trumpnominated Fed governor Jerome Powell to succeed Fed Chairwoman Janet Yellen when her term expires in February.