Kansas coach Bill Self answers a question near his Associated Press Coach of the Year trophy at a news conference at the NCAA Final Four college basketball tournament Thursday, March 31, 2016, in Houston. (AP Photo/David J. Phillip)

The recent report that the coach-shopping Houston Rockets were “intrigued” by Big 12 bosses Bill Self and Shaka Smart served as a reminder that all good things come to an end. Eventually, although not likely any time soon, Self will probably want to take a crack at coaching the best basketball players on the planet and see if he can join one-time mentor Larry Brown as the only coaches to win NCAA and NBA titles.

Just as every athletic director has a list of coaching prospects for every sport in the event of an unexpected departure, every NBA GM has a list of prospective candidates. Self is on plenty of those lists, which doesn’t mean the feeling is mutual.

Before hiring David Blatt in advance of the 2014-15 season, the Cleveland Cavaliers had Self’s name at the top of their wish list and moved on upon finding out he did not have any interest in leaving his job as basketball czar at Kansas University, a job for which he successfully campaigned during the 2003 Final Four in New Orleans.

The Cavs hired since-fired David Blatt on June 21, 2014, and LeBron James rejoined his original organization three weeks later.

Self is on a recruiting roll at Kansas, having landed Josh Jackson, No. 1 in the Class of 2016, per Rivals. The top four 2017 prospects — DeAndre Ayton, Michael Porter, Mohamed Bamba and Wendell Carter — all list Kansas among their schools of interest.

Clearly, Kansas is not in imminent danger of losing its coach. Nevertheless, an AD must always have a list of names in his pocket, more specifically in the iPhone in his pocket. The list can be as small as five, as large as 15, but the list must exist. Always. And it must be updated frequently.

My subject-to-change list, listed in alphabetical order, has nine candidates (school, career NCAA Tournament record):

John Beilein (Michigan, 17-10): Widely regarded as one of the greatest offensive minds on the planet, Beilein has taken Canisius, Richmond, West Virginia and Michigan to the NCAA Tournament. In a three-season span (2011-13) at Michigan, Beilein won two Big Ten championships, and in the year he didn’t (2011-12), he took his team to the Final Four. That happened the year that Elijah Johnson could have extended the game with a wide-open layup and instead fired a pass to Naadir Tharpe, whose only option was a desperation heave from way beyond the three-point line.

Beilein, 63, is an exceptional coach and solid recruiter.

Tad Boyle (Colorado, 1-4): The former Kansas guard has taken Colorado to the NCAA Tournament four times in the past five seasons. In the 42 seasons before that run started, the Buffs made the tournament twice (1997, 2003).

Boyle is a fiery competitor and has that rare ability to make a person he just met feel as if he’s known him his whole life. That connecting quality and competitive nature convince me he could recruit blue-chippers to Kansas.

Fred Hoiberg (Chicago Bulls, 4-4): He’s not looking to leave the NBA, but as impatient as franchises are in that league, it’s worth keeping a close eye on the former Iowa State coach. Former Butler coach Brad Stevens, on the other hand, is very secure with the Boston Celtics and therefore is not on the list.

Chris Mack (Xavier, 7-6): The most underrated coach in America. Has maintained the level of success established by current Arizona coach Sean Miller, one of Macks’ bosses at Xavier (Skip Prosser was another). Has taken Muskateers to six NCAA tournaments in seven seasons and had his team ranked as high as eighth in 2011-12 and fifth this past season. Last team to defeat national champion Villanova.

Danny Manning (Wake Forest, 0-1): His impressive work at Tulsa earned him a quick promotion to the ACC, where he routinely battles schools with elite basketball traditions. Manning’s a direct communicator with a great basketball mind, which is why he can take on anyone given equal talent. Whether he can recruit equal talent is all he has left to prove.

Gregg Marshall (Wichita State, 10-12): Routinely shafted by the NCAA Tournament committee with far worse seeds or bracket placements than his teams deserve, Marshall consistently gets the best out of his aggressive teams.

The Shockers have made five consecutive NCAA Tournaments, reached the Final Four in 2013, went 35-1 in 2014 and lost in a classic cliffhanger to national runner-up Kentucky, knocked off Kansas in 2015 and in this past tourney defeated Vanderbilt and Arizona before losing to Miami. At Winthrop, his teams made the tourney seven of nine seasons.

Archie Miller (Dayton, 5-3): Son of legendary Pennsylvania high school coach John Miller and brother of Arizona’s head coach, the guess here is that history will remember Archie as the best coach in the family. A former sharpshooter at North Carolina State, Miller has coached Dayton to three consecutive NCAA Tournament appearances, including all the way to the Elite Eight in 2014.

Rick Pitino (Louisville, 53-18): There is a reason names such as Duke’s Mike Krzyzewski, Michigan State’s Tom Izzo, Kentucky’s John Calipari and UConn’s Kevin Ollie did not make this list. No point in including coaches you know wouldn’t leave for another college job, just as Self never would leave Kansas for a competitor.

Pitino just might be open to one more landing spot before he retires. No other coach has won a national title at two schools (Kentucky and Louisville). Winning one at a third school would vault Pitino into third place on the all-time college basketball coaching list, ranking behind only John Wooden and Coach K.

Mark Turgeon (Maryland, 8-7): After rebuilding Wichita State, Turgeon coached Texas A&M into the NCAA Tournament in each of his four seasons there. Since recovering from an initial rush for the door by transfers, Turgeon has recruited well enough to have his Terps ranked as high as eighth in 2014-15 and second this past season.