The 29-year-old signed in 2005 from Italian club Reggina and has made no secret of his desire to finish his career at the Nissan Stadium, where he started his career when J-League side Marinos was known as Nissan FC.
While the fans' favourite's contract expires at the end of this season, the Hoops have a 12-month option to retain his services.
"I've told him that this club is suited to him and that it's a dream club for a player like him.
"He absolutely loves it here and he knows how much the fans, the players and the coaches love him."
However, although Strachan will urge Bhoys chief executive Peter Lawwell to make every effort to hold onto Nakamura, the fiery Scot admitted that he won't stand in the player's way when the time is right for him to return to his homeland.
Strachan added: "I know Naka does not want to go back home when he is unable to perform as he can. But he's incredibly fit.
"Naka's still under contract and we need him to stay for another year.
"If he decides after that to go home and play his football, then we will hold our hands up and say 'fine', because what he has done here has been absolutely beyond the call of duty."