The J-League club claimed they were planning a move for the midfielder who h as seen his appearances curtailed this season by injury.
"If he comes back to Japan, we, the Marinos, would like to stand for the candidacy as his next destination, but mothings has been decided," said Katsunori Nakamura, general manager of the Marinos.
"I think there will be the moment that I will have to go to Scotland for talks about this, but not now and not in January. I'd like to visit Celtic when the time comes."
Celtic however have no intention to sell the 2006/07 Scottish Player's Player of the Year and chief executive Peter Lawell confirmed they will be looking to extend his contract further.