The talks between the free agent starter, who has pitched for the Washington Nationals his entire career, and the Tigers are "serious," according to the report.
A two-time All-Star, the 6-foot-2, 225-pound Zimmermann won 19 games in 2013, tied for most in the National League. On the final day of the 2014 season, he no-hit the Miami Marlins, becoming the first pitcher in Nationals history to toss a no-hitter.
In 2015, he went 13-10 with a 3.66 ERA and made a career-high 33 starts.
Zimmermann is the Nationals' all-time leader in wins, innings, strikeouts and games started. He's one of just four pitchers to work at least 190 innings and make 32 starts in each of the past four seasons. His 810 innings pitched over that time ranks third in the NL, behind only Clayton Kershaw and Madison Bumgarner.
ESPN.com senior writer Eddie Matz contributed to this report.