McLeod and Picollo are the only known candidates after former Blue Jays GM Alex Anthopolous removed himself from consideration. Former Red Sox general manager Ben Cherington also declined an interview, according to the Minneapolis Star Tribune.
Cubs general manager Jed Hoyer confirmed on Monday that the Twins asked permission to interview McLeod, who is Chicago's senior vice president of player development and amateur scouting. But Royals GM Dayton Moore wouldn't confirm whether Picollo had already interviewed for the position when Kansas City played at Target Field last week.
"It would be inappropriate for us to discuss the general manager search of another team, but I will say that J.J. has been an important part of our success," Moore said. "And we've been very supportive of our people when they have opportunities."
The Twins are looking to emulate the structure of organizations such as the Cubs, who have a president of baseball operations and a general manager. Minnesota plans to hire a president of baseball operations who will hire a GM.
Picollo, who holds the title of vice president/assistant general manager of player personnel, has been with the Royals since 2006, coming over from the Braves with Moore. Picollo was Atlanta's director of Minor League operations. He's also worked as an area scout supervisor. Picollo is considered a key part of the front office that helped lead Kansas City to two straight World Series, including last year's title.
Picollo, 45, was a finalist for the Phillies' GM opening last year before that team hired Matt Klentak. Picollo played at George Mason University, getting drafted three times and playing five games in the Minors for the Yankees in 1994.
The Twins have kept their search for Terry Ryan's replacement quiet, but are believed to have a long list of candidates and reportedly have begun to interview them. Ryan was dismissed as GM in July.
Rhett Bollinger has covered the Twins for MLB.com since 2011. Read his blog, Bollinger Beat, follow him on Twitter @RhettBollinger and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.