Yokohama Marinos, the midfielder's first club, have expressed a desire to take the 29-year-old back to his homeland.
But Celtic chief executive Peter Lawwell has the option of a one-year extension to Nakamura's contract when it expires in the summer.
Nakamura said: "I do not want to finish my career away from home.
"Marinos were the club where I started my professional career so it would be great if I could go back there one day.
"But I will only go back when Peter says he does not need me here any more."
Nakamura made a goalscoring return to action on Saturday following three months out with a knee injury when he curled home from 25 yards to seal a 3-0 Scottish Cup win over Stirling.
And he admitted he was desperate to get back on the Parkhead pitch to ease the creative burden on Aiden McGeady.
"It was so exciting to return because I got so much applause from the fans," he said.
"I don't think the team was struggling when I was not playing but Aiden has been really good and having great performances.
"So if I can do the same things on my side of the pitch that may make things easier for Aiden."