According to newspaper Sports Nippon, the 22-year-old was first spotted by Chelsea last May and made a formal approach for the player in March.
FC Tokyo club president Naoki Ogane confirms that they have had an offer for the Japanese international.
"It is true that Chelsea sent us an offer for Muto," Ogane told Sports Nippon. "It is a formal offer with conditions. They want to acquire him in the summer"
Muto must still decide whether he wants to move to Stamford Bridge or not.
"I have not decided yet at all," he added. "It is an honour for me to receive this offer from a great club."