Molitor reportedly interviewed for the position more than two weeks ago, at which time he was considered the front-runner in the Twins' search.
The Hall of Famer joined the Twins' staff before this season as a coach overseeing baserunning, bunting, infield instruction, positioning and helping with in-game strategy. He became the team's first-base coach in July.
Molitor also served as a major league coach and minor league instructor in the organization for multiple years dating to 2000 and spent the final three seasons of his playing career with Minnesota from 1996-98.
Over his 21-year playing career, Molitor made seven All-Star teams, had 3,319 hits and finished with a .306 batting average and .817 OPS. He was a major candidate for the manager job when it opened upon Tom Kelly's retirement in 2001 but turned it down due to fears over contraction.
It was reported Thursday that Minnesota interviewed Toronto Blue Jays bench coach DeMarlo Hale for the manager job. The team has also interviewed Boston Red Sox coach Torey Lovullo, Chicago White Sox third base coach Joe McEwing and former Twins first baseman Doug Mientkiewicz.
The Twins fired manager Ron Gardenhire at the end of this season after 13 years on the job.
Gardenhire led the team to six playoff appearances, all in his first nine seasons as manager, and helped Minnesota advance as far as the 2002 ALCS. The Twins, though, haven't won a playoff game since 2004, haven't made the playoffs since 2010 and have had 92 losses or more in the four seasons since.
Minnesota went 70-92 this season and finished in last place in the American League Central.
The Twins' exact timeline for hiring a new manager is unknown.