Free-agent right-hander Lance Lynn turned down a two-year, $20 million contract offer from the Twins, according to the St. Paul Pioneer Press.
Lynn, 30, posted a 3.43 ERA in 33 starts for the Cardinals last season. He missed the entire 2016 campaign recovering from Tommy John surgery, though he proved durable in his return. In six seasons with St. Louis, he posted a 3.38 ERA with 8.5 K/9 innings.
Lynn is one of several notable pitchers remaining on the free-agent market, including right-handers Jake Arrieta and Alex Cobb.
The Twins had pursued Yu Darvish and other frontline free-agent starters during the offseason, but saw Darvish sign with the Cubs.