The Scottish press had reported that the Italian club had made a swoop for the 30-year-old player.
"We want to build a great team at Bologna and the first new face I want on board is Nakamura," club president Alfredo Cazzola told the Scottish Daily Record.
But Celtic later dismissed the speculation as "erroneous reports."
A Celtic spokesman said: "We've never heard of the representative who has claimed Bologna has made an offer for Shunsuke Nakamura.
"We have not received any offer from Bologna or from any other club. In any case Naka is delighted to be staying with Celtic and that is what he will be doing."