Celtic hope to persuade star midfielder Shunsuke Nakamura to stay with the club until the end of the season.
Nakamura has indicated he wants to return to his native Japan and could leave in the January transfer window.
"Celtic would be more than happy for Shunsuke to stay as long as he wants," said chief executive Peter Lawwell
"Certainly we want him to remain here until the end of the season. But his agent has intimated Shunsuke would like to return to Japan at some point."
The player's contract runs out at the end the current campaign, although Celtic have an option to extend for another season.
But the Japan international says he wants to go home for the good of his family after three years in Scotland.
"A move in January might be possible, I leave things like that to my agent," said Nakamura.
"If I was Scottish, I'd love to play at Celtic forever, but I'm Japanese and I also have a family and kids."
Nakamura, one of Japan's top sports stars, joined Celtic from Italian Serie A club Reggina in August 2005.
In his second season, he was voted Scotland's player of the year by his fellow professionals.
Celtic manager Gordon Strachan decided to rest Nakamura on the bench for Saturday's 4-2 win over Motherwell after he turned out for Japan in their World Cup qualifier in Bahrain last week.
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And the player highlighted his continued involvement with his country as another reason for wanting to leave Scotland.
"I've also had to think about the national team as well and I'm finding it quite hard travelling back and forward all the time," Nakamura said.
"When I take everything into consideration, it makes me thing I might need to go back to Japan."
The player says his agent has been speaking with a number of J-League clubs about a possible transfer.
But it is widely believed the front-runners for Nakamura's signature are his former club, Yokohama F Marinos.
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