Muto moved to Mainz in 2015 after starring in the J League for FC Tokyo.
The forward made a total of 71 appearances for the Bundesliga side, scoring on 23 occasions.
And he is now gearing up for a Premier League switch after agreeing terms with Rafa Benitez's team.
"News on Yoshinori Muto. The Japanese is about to change Mainz for Newcastle," the club announced on Twitter.
A statement from Mainz added: “Yoshinori Muto will not return to the Bruchweg as planned on Friday after his extended World Cup vacation.
“The Japanese striker is facing a possible move to England in the Premier League.
“The clubs are, as far as the terms of the contract, largely agreed, however, are around the change still time-consuming formalities to be done.”
Muto would be the fourth new face at St. James' Park this summer, after Newcastle confirmed the signing on Fabian Schar on Thursday.
Sparta Prague goalkeeper Martin Dubravka and ex-Swansea midfielder Ki Sung-Yeung have also arrived, while Mikel Merino and Chancel Mbemba are the two highest-profile Magpie departures so far.