Fox Sports first reported the negotiations Saturday night, citing sources that characterized the talks as "serious."
The 29-year-old Zimmermann would fulfill a clear need for the Tigers, a club searching for starting pitching. The Tigers entered the offseason intent on acquiring a pair of pitchers to round out their starting rotation.
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 against the Miami Marlinshe became the first pitcher in Nationals history to toss a no-hitter.
Zimmermann is the Nationals' all-time leader in wins, innings, strikeouts and games started. He is one of 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's Katie Strang and Eddie Matz contributed to this report.