President-elect Donald Trump has not extended an offer to retired neurosurgeon and former presidential rival Ben Carson to head the Department of Housing and Urban Development, a Carson spokesman said on Wednesday, disputing a report by The Wall Street Journal.

"Trump did not make an offer," Carson spokesman Armstrong Williams told Reuters. "He asked him to consider HUD. Nothing has been offered and no decision has made."

The Wall Street Journal earlier had cited Williams as saying Carson had been offered the post and had accepted.

"@realDonaldTrump is considering @RealBenCarson for a cabinet post. Dr. Carson is prayerfully & seriously considering," Armstrong said on Twitter. On Tuesday, Armstrong had told Reuters that Trump had asked Carson to consider taking the post and that Carson was considering it.

As recently as last week, Carson, 65, had told The Washington Post he was not interested in a Cabinet job, saying, "Having me as a federal bureaucrat would be like a fish out of water."

But he and Trump met on Tuesday at Trump Tower in New York, and earlier on Wednesday Carson posted on Facebook that after the talks he felt "that I can make a significant contribution particularly to making our inner cities great for everyone."

Fox News' Brian Kilmeade, sitting in as a guest co-host on "The Five," speculated that Carson has the job, but likes to tell the truth when asked about it and may have let the news slip before the Trump team made the official announcement.

Carson is a retired surgeon who dropped out of the race for the Republican nomination and backed Trump.

Carson initially indicated he would consider the post over the Thanksgiving holiday weekend, but said Wednesday morning to expect an announcement "soon."

Two other members of Trump's Cabinet were announced on Wednesday. South Carolina Gov. Nikki Haley was announced for U.N. ambassador, and school choice advocate Betsy DeVoss was announced as his pick for Education secretary.