Wataru Endo made four appearances for Japan at the 2022 World Cup
The 30-year-old made 33 Bundesliga appearances last season, scoring five goals and registering four assists.
Stuttgart narrowly avoided relegation last season by winning a play-off against Hamburg.
Liverpool have moved for Endo after missing out on Ecuador international Moises Caicedo, who has joined Chelsea from Brighton in a £115m deal.
The Reds are also set to be beaten by Chelsea to the signing of Southampton's Belgian midfielder Romeo Lavia, 19.
Liverpool want a defensive midfielder following the departures of Fabinho, Jordan Henderson and James Milner this summer, while fellow midfielders Naby Keita and Alex Oxlade-Chamberlain have also left the club.
Endo, who has 50 caps for Japan, joined Stuttgart initially on a season-long loan in 2019 before completing a permanent deal.
He was in Japan's squad at the 2022 World Cup and helped his country defeat Germany and Spain on the way to finishing top of their group. They were beaten by Croatia on penalties in the last 16.
Despite Stuttgart's struggles last season, Bundesliga's statistics put Endo fourth in terms of duels won last season and seventh when it came to distance covered.
He also played in Stuttgart's German Cup win against TSG Balingen last Saturday, scoring the final goal in a 4-0 win.
-- Courtesy of BBC Sport