Federal Reserve Governor Lael Brainard on Tuesday said that while inflation is too high and getting it down is the U.S. central bank's most important task, there are some signs of "welcome" cooling.

"I'll be looking to see whether we continue to see moderation in the months ahead," Brainard told the Wall Street Journal in an interview, referring to inflation in the 'core' goods category. She also said she expects demand to moderate this year as fiscal support moderates and supply constraints ease.