Il Corriere dello Sport says Milan will have competition from Chelsea.
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However, the 23-year-old doesn't want to consider his future just yet.
"I want to become one of the best goalkeepers in the world, and I am very focused on Parma and the World Cup," said Suzuki.
"I am a calm person, a goalkeeper always has to be. I cover the goal and I can play with my feet. I work every day to improve myself in all aspects."
His contract with Parma runs until 2029.