According to ESPN's Adrian Wojnarowski, Messina will be among those interviewed for the vacancy in Milwaukee. Former Charlotte Hornets coach Steve Clifford and ex-New Orleans coach Monty Williams will also discuss the position with the team.
After spending the early part of his career as a head coach overseas, the 58-year-old has served as an assistant in San Antonio for the past four seasons.
Messina filled in as Spurs head coach for the final three games of the team's first-round series against the Golden State Warriors when Gregg Popovich took a leave of absence following the death of his wife, Erin. San Antonio went 1-2 under the interim coach.
Spurs players believe Messina has earned a shot to lead his own team.
"I think the time has come," guard Manu Ginobili said at the end of the season, via Tom Orsborn of the Houston Chronicle. "For sure, he's very capable and experienced."
Ginobili wasn't the only one who showed support. Six-time All-Star and two-time champion Pau Gasol also wants to see Messina land a head-coaching gig, via Orsborn:
"He handled it very well, with great composure. He handled the adversity and also the opportunity really well. He sent the right message to the team coaching the right way. He was always sharp and in control of the situation. He did a good job.
"Messina has been one of the top head coaches in Europe. It's hard to get that opportunity in the NBA, but if there's someone who should get it, it should be him."
Players don't typically have a say in personnel decisions (especially for opposing teams), but getting endorsements from notable players like Ginobili and Gasol can't hurt Messina's cause.
The 2017-18 season was supposed to see Milwaukee go from a young team with promising talent to a serious Eastern Conference contender. Instead, Jason Kidd was fired after a 23-22 start to the 2017-18 season. Joe Prunty went 21-16 as interim coach, leading the team to the seventh seed.
Although they were ultimately eliminated, the Bucks managed to take the Boston Celtics to seven games in the first round of the 2018 NBA playoffs. It marked their fourth opening-round exit in six seasons, missing the postseason entirely in the other two campaigns.
Now, Milwaukee is looking for a coach to push the team to the next level.