"Shunsuke is a legend," Lawwell told the Sports Hochi paper. "We hope Naka will play at Celtic as long as possible. A contract period? It's as long as he wants."
However, the Daily Mail says the SPL champions face an uphill battle to convince Nakamura to remain in Scotland beyond this season.
Informal talks took place by telephone last week, when it was intimated to Celtic that the midfield playmaker harbours ambitions to return home to Japan next season, despite interest from English and Spanish clubs.
Yokohama Marinos, Nakamura's hometown club, are believed to have hatched plans to bring their prodigal son back to the Land of the Rising Sun sometime in the next 12 months.