The 22-year-old was also wary about qualifying for a work permit to play in England, Kyodo quoted an unnamed official at Muto's current club FC Tokyo as saying.
Muto scored 13 goals for Tokyo last season and only graduated from Keio University in March after completing an economics degree.
Mainz are currently 12th in the Bundesliga and have enjoyed success with Japanese strikers. Shinji Okazaki is their top scorer this term.
Chelsea, who announced their 'largest ever commercial deal' with Japanese tyre firm, Yokohama Rubber Company earlier this year had bid around 700 million yen (£3.7 million) for Muto in March, Kyodo said.
Muto, who has notched eight goals in 11 league games this term, is with the national team on a two-day training camp. He was expected to reveal his transfer plans on Thursday, Kyodo said.
(Writing by Patrick Johnston in Singapore; Editing by John O'Brien)
