Nakamura is still under contract with Celtic until 2009, but the Japanese club believe their hand is strengthened by the fact that the player's agent, Roberto Takuda, who said: "Shunsuke has never forgotten what the J League did for him and he wants to repay that and show what he has learned in Europe sooner rather than later.
"Marinos are his first choice. If that doesn't come around it depends on the other offers on the table."
A spokesman for Yokohama said: "When a player of that class shows he has an inkling to come back to Japan we have to put our hands up. Another club's strip would not suit him."