The White House has notified Powell that it intends to nominate him, the WSJ reported, citing a person familiar with the matter.
Figuring out who the administration would name to succeed current Fed Chair Janet Yellen has been one of Wall Street's favorite parlor games in recent weeks. Powell has long been seen as a front-runner along with former Fed board member Kevin Warsh, Stanford economist John Taylor and Yellen herself.
Trump is slated to announce his decision on Thursday, before he leaves for a trip to Asia on Friday. The WSJ report said the president had settled on his selection on Saturday but could change his mind.
Yellen's four-year term expires in February. She took over as Fed chair in 2014 under President Barack Obama, succeeding the departing Ben Bernanke.
Powell has been seen as the "safe choice" to succeed Yellen because he is not expected to veer drastically from current Fed policy. On Wednesday, the Fed left interest rates alone, though expectations are that it will raise rates at its next meeting in December.