Celtic appear resigned to losing Shunsuke Nakamura - but they are hoping to persuade him to stay until the end of the season.
The Japan midfielder, 30, has hinted he may quit the Scottish Premier League champions during the January transfer window.
Nakamura's contract expires in the summer, although the club have an option to extend his stay for another season.
However, the player is finding travelling between Glasgow and Japan for international duty increasingly difficult and he wants to return home for the sake of his young family.
Hoops chief executive Peter Lawwell will try to convince him to see out the current campaign but may be fighting a losing battle.
"Celtic would be more than happy for Shunsuke to stay here for as long as he wants and certainly we want him to remain here until the end of the season," Lawwell said.
"But his agent has intimated Shunsuke would like to return to Japan at some point."