The Twins announced Saturday that Duda and Rosales had been invited to big league spring training.
Duda hit a combined .241 with 14 home runs and 50 RBI for Kansas City and Atlanta last season. The 33-year-old is a career .242 hitter with 152 homers in nine seasons, including 30 home runs for the New York Mets and Tampa Bay in 2017.
If added to the 40-man roster, the 35-year-old Rosales would get a one-year contract paying a $1 million salary while in the major leagues.
Rosales hit .211 in 13 games for Cleveland last year. He is a career .226 hitter with 48 home runs and 179 RBI in 11 years with Cincinnati, Oakland, Texas, San Diego, Arizona and Cleveland.
Rosales has split time at all four infield spots.