The Twins, however, have not responded to the reports. When reached by phone, Twins interim general manager Terry Ryan said the club "has nothing to announce."
Carroll, who turns 38 in February, hit .290 with a .359 on-base percentage and .347 slugging percentage in 146 games with the Dodgers last season. He also stole 10 bases without getting caught.
Known for his steady defense, Carroll saw time at both second base and shortstop last season, and has also played third base and both corner outfield positions. According to an industry source, Carroll would likely be the everyday shortstop and figures to slot in the two-hole.
The 10-year veteran is a career .278/.356/.347 hitter and hasn't posted an on-base percentage lower than .346 since 2007. He's not a ranked free agent, meaning he would not cost the Twins a Draft pick if signed.
Carroll would fit the club's need in the middle infield after the struggles of Tsuyoshi Nishioka and Trevor Plouffe at shortstop, especially defensively, last season.
It would also represent Ryan's first signing since taking over as interim GM on Monday, when he replaced Bill Smith.
Additionally, the Twins also announced they signed right-hander Jared Burton and outfielder/infielder Brian Dinkelman to Minor League deals with invites to spring training. Burton, 30, pitched with the Reds the last five seasons, posting a 3.41 ERA with 143 strikeouts and 73 walks in 169 innings pitched. He tossed just 4 2/3 innings with the Reds last season, allowing two runs, as he missed most of the season with a shoulder injury.
Dinkelman, 28, played in 23 games with the Twins, hitting .301 with one double and four RBIs in 23 games. He also hit .243 with three homers, 41 RBIs and seven stolen bases in 127 games with Triple-A Rochester, but was outrighted after the season.