The Japanese international striker made just one appearance for his nation at the World Cup, but has experience in international football after gaining 25 caps for the 'Blue Samuari'.
He currently plays his club football for German side Mainz, and has scored 20 times in 66 matches since joining the club in 2015.
'Sky Sports' reports that Newcastle have agreed to pay a fee of £9.5 million to secure his services, and that he will make his way to Newcastle to complete a medical once he has received a work permit.
Rafa Benitez's side were severely lacking goals in the Premier League last season, with Dwight Gayle potentially moving to Stoke City and Aleksandar Mitrovic looking for a permanent move to Fulham.
Muto would be the fifth signing by the 'Magpies', after they confirmed the acquisition of Fabian Schar on Thursday.