According to reports in the Scottish media, Nakamura's agent Roberto Takuda has informed Celtic that his client will not be the subject of a bid from J.League club Yokohama Marinos, as had been anticipated.
Celtic would have insisted on a fee to release the 30-year-old and, but Yokohama are reportedly prepared to wait until the playmaker becomes a free agent at the end of the 2008/09 campaign.
Celtic's interest in European competition ended last week, when a defeat by Danish side Aalborg condemned them to finishing last in their UEFA Champions League group.
Nakamura, who has helped Celtic win three Scottish titles since arriving at Parkhead in 2005, refused to comment on his future in the aftermath of that defeat, fuelling a belief he would quit Glasgow for Japan in time for the start of the new J.League season in March.
Celtic manager Gordon Strachan, however, has repeatedly voiced confidence that the left-footed player would stay until May and possibly even longer.
"I don't think the fact we are no longer in Europe alters things one little bit in respect of Naka," Strachan said earlier this week. "You have never seen a happier man than him in training."