Ben Carson. Chip Somodevilla/Getty Images

President-elect Donald Trump tweeted on Tuesday he's "seriously considering" retired neurosurgeon and 2016 presidential candidate Ben Carson to be the secretary of housing and urban development in his administration.

Carson has repeatedly affirmed he is not looking to serve inside a Trump administration. He was previously rumored to be under consideration for secretary of education and secretary of health and human services.

"I am seriously considering Dr. Ben Carson as the head of HUD," Trump wrote. "I've gotten to know him well — he's a greatly talented person who loves people!"

Carson will meet with Trump at Trump Tower on Tuesday, according to MSNBC.

The Hill reported last week that Armstrong Williams, Carson's business manager and close confidant, said Carson wouldn't join the administration and would instead be an unofficial adviser after reports surfaced that Carson rejected an offer to be HHS secretary.

"Dr. Carson was never offered a specific position, but everything was open to him," Williams told The Hill. "Dr. Carson feels he has no government experience; he's never run a federal agency. The last thing he would want to do was take a position that could cripple the presidency."

Carson subsequently published a Facebook post disputing what Williams attributed as his reason for not seeking a position.

"My decision not to seek a cabinet position in the Trump administration has nothing to do with the complexity of the job as is being reported by some news outlets," he wrote. "I believe it is vitally important for the Trump administration to have many outspoken friends and advisers who are outside of the Washington bubble. It is vital to have independent voices of reason and reconciliation if our nation is to heal and regain its greatness. I will continue to work with the transition team and beyond as we build a dynamite executive branch of government."

In an interview with Business Insider just before the election, Carson said, "I don't want to be a part of the administration."

"Not that I have anything against it," he said. "Just that I think my voice will actually be more valuable outside the administration. There are so many issues that affect our country right now, and we can't lose sight of them. So winning the election is really just step one."

"I'll continue to write, continue to speak publicly, and work on helping to focus us as a nation on what's really important," he said.

In a Monday Facebook post, however, Carson seemed to signal a shift in his thinking, although he wrote "there is no reversal of my position in terms of working with the Trump administration."

"I have always made it clear that I preferred to work outside of the government as an advisor, but if called upon, I would serve inside of the government," Carson wrote. "I believe it is important to have voices that are outside of the administration combating media bias and the divisiveness that has infected our country."

Washington Post reporter Robert Costa tweeted shortly after Trump's tweet that Trump "has been relentless" in pushing Carson to reconsider his position from last week, when he said he was not interested in a Cabinet position.

Williams did not immediately respond to Business Insider's request for comment on Carson's stance.