The 26-year-old impressed on international duty for his country at the world Cup and Newcastle boss Rafa Benitez is now seemingly keen to push through a move.
The 'Magpies' have made strengthening their attacking options a priority this summer, with talks ongoing over a deal with West Brom that would see Salomon Rondon and Dwight Gayle swap places.
Muto is thought to be available for an initial fee of £9m, with a move looking much easier to complete than the Rondon swoop.
The 25-cap Japan international has made 66 Bundesliga appearances for Mainz since joining from FC Tokyo in 2015, scoring 20 goals and laying on 10 more.
Meanwhile, Newcastle also appear to be closing in on Deportivo defender Fabian Schar after invoking his release clause. Goalkeeper Matz Sels is close to tying up a £3.5m switch to Toulouse.