Bloom was also the Rays' director of baseball operations from November 2011 to October 2014, when he was promoted to his current position.
The Twins are searching for an executive to oversee their baseball operations department to replace former GM Terry Ryan, who was dismissed in July. Bloom joins Cubs vice president Jason McLeod and Royals assistant general manager J.J. Picollo as potential candidates.
McLeod, who has 21 years of baseball experience in baseball operations and coaching, helped rebuild the Red Sox and Cubs organizations under Theo Epstein. He also worked as a scout and Minor League coach during his nine-year stint with the Padres.
Picollo has been with the Royals since 2006 and was previously the director of Minor League operations with the Braves. Picollo helped lead Kansas City to two straight World Series, including last year's championship.
Former Blue Jays GM Alex Anthopolous was at one point considered a candidate for the position before removing himself from the running. The Twins also requested an interview with former Red Sox general manager Ben Cherington, which he declined, according to the Minneapolis Star Tribune.
Cherington accepted an offer to become the Blue Jays' vice president of baseball operations Wednesday.
Oliver Macklin is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.