With no agreement in place, Rafael Benitez took Mitrovic to Portugal, where Newcastle were playing a friendly against Porto on Saturday evening, but Press Association Sport understands the striker left the tour to head back to the United Kingdom after some common ground was reached.
The transfer fee is expected to be 9.5 million pounds (US$12.45 million) according to British media reports.
Muto's club went to the extent of issuing a statement saying that what remains for the deal to be completed are mere formalities.
Muto started out at FC Tokyo where he played 51 league games, scoring 23 goals, before joining Bundesliga side Mainz in 2015 (66 games, 20 goals).
Aleksandar Mitrovic shone for Fulham last season
The 23-year-old, who represented his nation in the World Cup in Russian Federation this summer, spent a fruitful loan spell there at the tailend of last season, scoring 12 goals in just 17 games as they earned promotion via the playoffs.
Muto featured once for his country at the World Cup in Russian Federation, starting and playing 82 minutes in the 1-0 group-stage loss to Poland.
Newcastle United finished 10th last season in England's top division.
The club has been busy this week, having also signed Switzerland defender Fabian Schar on a three-year deal on Thursday.