Ange Postecoglou brought Ideguchi back to the UK following a poor spell at Leeds United and was hoping to see the midfielder succeed second time round.
He has failed to make an impact at Parkhead though and is struggling to secure game time under Postecoglou.
Celtic are now looking at loan options for Ideguchi as they look to secure him minutes on the pitch.
It is unclear if Celtic are thinking about loaning the Japanese star to a club within Scotland or are looking further afield for a solution.
Ideguchi has made two matchday squads in the Scottish Premiership this season, but has been an unused substitute on both occasions.
He has made just six appearances for the Bhoys at senior team level since joining the club.
Celtic have him on a lengthy contract which is due to run until the summer of 2026.