Revere hit .294 with 32 RBIs, 70 runs and 40 stolen bases for the Twins in 2012. In his three-year career, Revere is hitting .278 with 127 hits and 74 stolen bases in 254 games for Minnesota.
Morosi suggests that the Twins would need to get back a center fielder in the deal that may send Revere elsewhere.
Revere's 40 stolen bases tied him with Jose Reyes for fifth in the league last season, just nine behind league-leader Mike Trout.
The Minnesota Twins also traded outfielder Denard Span to the Washington Nationals in exchange for right-handed pitcher on Alex Meyer on Nov. 29.
Minnesota is reportedly searching free agency and trade options to acquire starting pitching this off-season.
The Twins finished fifth in the AL Central with a 66-96 record.