The 20-year-old, who is seen as one of Turkey's best young prospects, was linked with Premier League clubs Middlesbrough and Newcastle.
However, the Turkish international will be staying put - his agent Ahmet Bulut has explained.
"We know of some interest, but he will not be leaving the club before the European finals," Bulut said.
"I do not want to say which clubs want him, but from what I know there is nothing from either of these clubs [Middlesbrough and Newcastle].
"He will not leave in January as Galatasaray are involved in the title race as they are currently second and are playing well."
Bulut admitted that Turan does want to play in England and has talked about the prospect with international team-mates Emre and Tuncay Sanli - who are coincidentally plying their trades in the North East for Newcastle and Middlesbrough respectively.
"Of course he knows all about England, he has talked with Emre and Tuncay about this," he continued.
"He has also seen it on television as the Premier League is huge over here."