WASHINGTON—The White House has notified Federal Reserve governor Jerome Powell that President Donald Trump intends to nominate him as the next chairman of the central bank, according to a person familiar with the matter.

The president spoke with Mr. Powell on Tuesday, according to another person familiar with the matter who couldn’t describe what they discussed.

Mr. Trump had settled on Mr. Powell by Saturday, but people familiar with the process had cautioned that he could change his mind. The president plans to formally announce the decision Thursday before he leaves for a trip to Asia on Friday.

Reached by phone Wednesday, both Mr. Powell and Fed Chairwoman Janet Yellen declined to comment. A Fed spokeswoman also declined to comment.