When asked if he was offered a position leading the Department of Housing and Urban Development, Carson said, "I would say that was one of the offers that’s on the table."
Cavuto asked Carson about his qualifications for the post.
"I know that I grew up in the inner city and have spent a lot of time there, have dealt with a lot of patients from that area, and recognize that we cannot have a strong nation if we have weak inner cities," Carson replied.
Carson's comments follow a Tuesday tweet from Trump saying he was considering Carson for the role.
I am seriously considering Dr. Ben Carson as the head of HUD. I've gotten to know him well--he's a greatly talented person who loves people!
— Donald J. Trump (@realDonaldTrump) November 22, 2016
Carson has already turned down Trump's offer to serve in the administration, according to a spokesman for Carson.