Hudson would fill the club's hole at second base and provide it with a natural fit in the No. 2 spot in the lineup.
Last season, Hudson batted .283 with 35 doubles, nine home runs and 62 RBIs for the Dodgers. He scored 74 runs and had an on-base percentage of .357.
Twins general manager Bill Smith declined comment when asked about Hudson on Thursday, keeping with his policy of not discussing specific players.
Hudson, 32, made a base salary of $3.38 million in 2009 with the Dodgers, but with incentives, he received close to $7 million. Hudson was thought to be looking for a guarantee closer to his actual '09 earnings, though the industry speculation has been that he'll have to take a pay cut.