Lynn, 30, was 11-8 with a 3.43 ERA as he rebounded to reclaim his spot as one of the Cardinals' most durable starters in 2017 after missing all of the 2016 season while recovering from Tommy John surgery.
A right-hander, Lynn hadn't pitched for St. Louis since the end of the 2015 season. He had elbow ligament replacement surgery shortly after that.
The price of a qualifying offer this year is $17.4 million. The offer can be made through the fifth day after the World Series, and a player has a week after that to accept.
Rosenthal, who recorded 93 saves in 2014-15, underwent season-ending Tommy John surgery on his right elbow in August. It came after he reclaimed the closer's job from Seung Hwan Oh earlier last season after Oh struggled. Rosenthal recorded 11 saves, giving him 118 over the past four seasons.