The $1 billion stadium is scheduled to open in time for the 2016 NFL season.
The bid will be for the years 2017-2020, for which there are eight finalists: Atlanta, Indianapolis, Minneapolis, New Orleans, North Texas, Phoenix/Glendale, San Antonio and St. Louis.
Minneapolis has previously hosted the Super Bowl in 1992 as well as the Final Four in 1992 and 2001. Major League Baseball's All-Star Game will be played at Target Field in Minneapolis on July 15.
The 2015 Final Four will be held in Indianapolis at Lucas Oil Stadium and NRG Stadium (previously Reliant Stadium) in Houston will be the site of the 2016 Final Four.
More from the Pioneer Press:
Typically, the NCAA likes to have sites that host the Final Four host an earlier round of the tournament the previous year, Michele Kelm-Helgen, chairwoman of the Minnesota Sports Facilities Authority said. That means 2017 is out. And in 2018 the stadium will host the Super Bowl. So most likely, the local bid will focus on 2019-20 for the Final Four, with preliminary rounds in earlier years, she said.