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 Jacob 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. Ace Ervin Santana is recovering from surgery on his right middle finger and will likely miss the first couple of months of the regular season, making potential additions to the rotation of more urgence for Minnesota.
The Twins acquired right-hander Jake Odorizzi in a trade with the Rays last month to bolster the rotation between Jose Berrios and Kyle Gibson. Beyond that trio, the Opening Day rotation is unsettled so far, with candidates such as Anibal Sanchez, Phil Hughes and Adalberto Mejia competing for the other slots.

Other clubs that have shown recent interest in Lynn include the Orioles, Brewers and Phillies.