Tommy Burns admits Shunsuke Nakamura may leave Celtic in two years' time.
Former Celtic boss Martin O'Neill, now at Aston Villa, this week dismissed reports he had made an enquiry about the Japanese playmaker.
But the 29-year-old, voted player of the year by his fellow professionals and Scotland's football writers, has plenty of admirers.
Burns told www.stv.tv: "Naka has come from a totally different culture. I think he's very happy here. His family's very settled here. That has been shown in the performances on the pitch.
"But I've no doubt that in the next two to three years there may be the opportunity for him to go and try something else.
"These guys are very cosmopolitan and they want to go and see different cultures. But I think at this moment in time he's certainly very happy here."
Burns suggested there are "a lot of untruths circulating" regarding Nakamura.
The Celtic head of youth development also admits goalkeeper David Marshall is desperate for a first-team role, which he is again likely to be denied next season by Artur Boruc.
The 22-year-old had a loan spell at Norwich which was ended by injury last season, and the arrival of Mark Brown from Inverness in January adds to the competition for Marshall, who could move again.
Burns said: "I think David is now looking to see where his future lies because he wants to go and play regular first-team football, so hopefully something can be agreed and it can suit both parties."