According to reports from The Mirror, Manchester United have been watching the Japan forward for sometime now, and are planning to make a formal bid for him once the transfer window opens next week.
Muto has a contract at Mainz until 2019, but the German club could be persuaded to sell him if United choose to bid.
The 23-year-old striker joined Mainz in May from FC Tokyo and has scored seven goals in 14 appearances for the Bundesliga club so far.
Louis van Gaal’s side have struggled for goals this season and the Dutchman knows he needs to strengthen his attacking options.