The Hoops believe the Japanese playmaker is enjoying his spell in Glasgow and not looking at other options.
Nakamura was named player of the year for 2006-07 by the Scottish Professional Footballers' Association, as well as by the football writers and league sponsors, as he helped Celtic to the domestic double and the last 16 of the Champions League.
To lose him would be a major blow, but Celtic are confident Nakamura will not be seeking a transfer.
A club spokesperson said: "Celtic have a contract with Nakamura for next year and the option for a further year.
"We have been give no indication he wishes to leave the club."
While they remain optimistic, the club have declined to comment on reports that a clause in Nakamura's contract could allow him to leave for £1million.
Italian agent Angelo Massoni believes Nakamura could be able to move for the price, which represents a fraction of his full value, and claims talks with Celtic could happen shortly.
Massoni claims "four of the biggest clubs in world football" have shown interest in Nakamura, who joined Celtic from Reggina in 2005.