Ben Carson as Trump’s Running Mate? Don’t Count Him Out Just Yet.

Just about the only person who shows any interest in Ben Carson as the Republican vice-presidential nominee is the one whose opinion matters the most: Donald J. Trump.

Mr. Carson, the retired neurosurgeon and former housing secretary in Mr. Trump’s administration, is under consideration as one of “many people that would do a really fantastic job,” the former president told a local New York reporter last month.

Last week, Mr. Trump again highlighted the possibility of running with Mr. Carson, saying on Newsmax that he was among “many great people.”

And behind closed doors, Mr. Trump has spoken warmly of Mr. Carson, reflecting an odd-couple political friendship between the belligerent Republican leader and the soft-spoken doctor who ran against him in 2016.

That personal connection, which has deepened over the years, is why Mr. Carson continues to linger as a potential choice for Mr. Trump’s running mate even as the race shows signs of narrowing to a few top candidates including Doug Burgum, Marco Rubio and J.D. Vance.

Few people close to the former president give Mr. Carson much chance of being chosen. But given Mr. Trump’s unconventional approach and history of last-minute decisions, a surprise is possible — and in the wide universe of unlikely but he-just-might-do-it picks, Mr. Carson is probably the leading contender.